Here you are! You can open a fitness centre and run a course : no food, no water, no stop! More math, less fat hahaha~ Q1. Sum of 1/n, 4:17 Q2. Sum of 1/ln(n), 11:30 Q3. Sum of 1/ln(n^n), 17:23 Q4. Sum of 1/(ln(n))^ln(n), 23:00 Q5. Sum of (-1)^n/arctan(n), 32:04 Q6. Sum of 2^n/(3^n+n^3), 35:47 Q7. Sum of 3^n/(2^n+n^2), 39:01 Q8. Sum of n*sin^2(n)/(n^3+2), 46:17 Q9. Sum of (-1)^n/sqrt(n+1), 49:31 Q10. 1/2-1/3+2/9-4/27+... 55:31 Q11. Sum of (1/sqrt(n)-1/n), 58:21 Q12. Sum of 1/n^2ln(n), 1:03:28 Q13. Sum of 1/sqrt(n)e^sqrt(n), 1:06:54 Q14. Sum of n^n/3^n^2, 1:19:03 Q15. Sum of n^n/(n!)^2, 1:22:06 Q16. Sum of nsin(1/n), 1:28:05 Q17. Sum of 1/(n+3^n), 1:32:09 Q18. Sum of sin(2n)/(n+3^n), 1:34:02 Q19. Sum of n((-1)^n)/(3n+1), 1:36:27 Q20. 1/2+1/6+1/12+1/20... 1:38:28 Q21. Sum of (n!)/e^(n^2), 1:42:52 Q22. Sum of (n^2 + 1)/(n^3 +1), 1:46:35 Q23. Sum of sin(1/n^2), 1:48:59 Q24. Sum of cos^2(1/n), 1:51:51 Q25. Sum of cos(pi x n)/ln(n), 1:53:33 Q26. Sum of (2n + 1)^n / [n^(2n)], 1:58:09 Q27. Sum of 1/2^[ln(n)], 2:00:35 Q28. Sum of 1/3^[ln(n)], 2:03:23 Q29. Sum of (3n^2 + n)/sqrt(n^5 + 2n + 1), 2:04:16 Q30. Sum of n/(2^n), 2:10:41 Q31. Sum of (n!)^2 / (2n)!, 2:17:43 Q32. Sum of 1 / [n^(1+1/n), 2:21:55 Q33. Sum of 1 / [n^(1 + 1/n^2)],2:26:40 Q34. Sum of 1, 2:30:10 Q35. Sum of n^2 / (2^n + 3^n), 2:30:58 Q36. Sum of (1 - 1/n)^n, 2:35:19 Q37. Sum of (1 - 1/n)^(n^2), 2:36:45 Q38. Sum of 1 / sin^4(n), 2:40:25 Q39. Sum of (n!)/(n^n), 2:41:45 Q40. Sum of 1/(n^3 + 3n^2 + 2n), 2:45:56 Q41. If sum of (an)^2 converges, then sum of an also converge, 2:52:52 Q42. If sum of an converges, then sum of (an)^2 also converges, 2:54:09 Q43. If sum of an converges, then sum of 1/(an) must diverge, 2:55:48 Q44. If sum of an diverges, then sum of 1/an must converge, 2:57:16 Q45. If sum of an converges, then sum of (an)/n must also converge, 2:58:40 Q46. If sum of an and sum of bn both converge, then sum of (an + bn) must converge, 3:00:10 Q47. If sum of an and sum of bn both diverge, then sum of (an - bn) must diverge, 3:01:41 Q48. If sum of an and sum of bn both diverge, then sum of (an x bn) must diverge, 3:03:55 Q49. If sum of an and sum of bn both converge, then sum of (an x bn) must converge, 3:05:57 Q50. Sum of 0, 3:08:15 Q51. Sum of n x sqrt[sin(1/n^2)], 3:08:52 Q52. Sum of [1 - sin(1/n)], 3:12:16 Q53. Sum of [1 - cos(1/n)], 3:18:05 Q54. Sum of 1 / cubert(2^n + 1), 3:22:51 Q55. Sum of 1/[sqrt(n) x ln(n)], 3:25:49 Q56. Sum of (n - 1)/sqrt(n^3 + 2n + 5), 3:26:32 Q57. Sum of [n^2 x 2^(n+2)] / 4^n, 3:32:00 Q58. Sum of [(nth root of 2) - 1], 3:36:55 Q59. Sum of [(nth root of 2) - 1]^n, 3:41:30 Q60. Evaluate sum of an, where a1 = 9 and an = (6 - n) x an-1, 3:43:23 Q61. Sum of [(n!)^n] / [n^(10n)], 3:46:23 Q62. Sum of [(2n)!] / n^n, 3:48:14 Q63. Sum of e^(-n) x sin n, 3:52:46 Q64. Sum of [tan(1/n)] / n^2, 3:56:58 Q65. Sum of (n^10 x 4^n) / n!, 4:01:53 Q66. Sum of (2^n x n!) / (n + 2)!, 4:04:58 Q67. Sum of 1 / sqrt(n!), 4:09:13 Q68. Sum of 1 / ln(n!), 4:11:24 Q69. Sum of [n(n+2)] / (2n+1)^2, 4:15:33 Q70. Sum of [e^(1/n) - e^(1/(n+2))], 4:16:57 Q71. Sum of (ln n) / n^2, 4:21:15 Q72. Sum of n^3 / (2n^5 + 3n - 4), 4:23:32 Q73. Sum of [(1-2n)/(3+4n)]^n, 4:24:54 Q74. Sum of (e^n) / [2^(2n-1)], 4:27:28 Q75. Sum of (n^3 - 2n - 1) / (2n^5 + 3n - 4), 4:30:02 Q76. Sum of 1 / (n + sqrt(n)), 4:33:12 Q77. Sum of 1 / (n x sqrt(n)), 4:35:15 Q78. Sum of sqrt(cos(1/n)), 4:36:10 Q79. Sum of (3^n x n^2) / n!, 4:37:45 Q80. Sum of n / (2^n), 4:41:09 Q81. Values of x for 1^x + 2^x + 3^x + ... + n^x + ... converge, 4:51:19 Q82. Values of x for x^1 + x^2 + x^3 + ... + x^n + ... converge, 4:53:08 Q83. Values of x for sum of (x - 2)^n / n^n converge, 4:54:39 Q84. Values of x for sum of (x^n) / n converge, 4:58:43 Q85. Values of x for sum of (x - 1)^n / (n x 3^n) converge, 5:04:18 Q86. Values of x for sum of (n!) x^n converge, 5:09:00 Q87. Values of x for sum of 1 / [x(ln x)^k] converge, 5:12:24 Q88. Values of x for sum of [1/(1 - x)]^n converge, 5:15:44 Q89. Values of x for sum of (sum of x^m)^n converge, 5:19:35 Q90. Sum of [(-1)^n] / (n!), 5:24:28 Q91. Sum of (pi/2 - arctan n), 5:25:34 Q92. Sum of sin^2 (1/n), 5:29:49 Q93. Sum of 1 / [sqrt n - sqrt(n+1)], 5:32:52 Q94. Sum of [1/sqrt n - 1/sqrt(n+1)], 5:35:55 Q95. Sum of 1 / e^(sqrt n), 5:38:16 Q96. Sum of 1 / [n x sqrt(n^5 - 1)], 5:43:35 Q97. Sum of ln[n/(n+2)], 5:46:12 Q98. Sum of 1/(e^n + 1), 5:49:23 Q99. Sum of 1/ln(e^n - 1), 5:50:42 Q100. 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ..., 5:54:20 Q101. Sum of (3^n x n!) / (n^n), 6:00:25
@@blackpenredpen at no.100 the integral of 1/1-x must be -ln(1-x) right? Cause if you differentiate 1/1-x you get 1/(1-x)^2 and what we previously had. Can please check it out and tell me if I'm mistaken? thanks in advance :)
@@Aravind-2906 no he isn't . If this was supposed to be a joke then he would have also changed his name to ramanujan. He is just a 12 yo who wants to look cool.
Just wanted to thank you. Anyone learning math needs to watch you. I've watched so many videos, and was still confused. It wasn't till I found your channel that I understood. Math makes sense!
I don't understand how i get exhausted after a one hour lecture in my college but left out more energetic after watching this video...Thank you so much for this .
I just watched this during my review for my Calc 2 finals. I understood the how the tests work and how and to what situations they are used through this video more than the notes and lectures in our online zoom classes. Thank you very much. It also was really fun while watching! I hope to see more of this in the future :D
Time stamps for you guys! Q1. Sum of 1/n, 4:17 Q2. Sum of 1/ln(n), 11:30 Q3. Sum of 1/ln(n^n), 17:23 Q4. Sum of 1/(ln(n))^ln(n), 23:00 Q5. Sum of (-1)^n/arctan(n), 32:04 Q6. Sum of 2^n/(3^n+n^3), 35:47 Q7. Sum of 3^n/(2^n+n^2), 39:01 Q8. Sum of n*sin^2(n)/(n^3+2), 46:17 Q9. Sum of (-1)^n/sqrt(n+1), 49:31 Q10. 1/2-1/3+2/9-4/27+... 55:31 Q10 to Q20. Thanks to "WHY IT" Q11. Sum of (1/sqrt(n)-1/n), 58:21 Q12. Sum of 1/n^2ln(n), 1:03:28 Q13. Sum of 1/sqrt(n)e^sqrt(n), 1:06:54 Q14. Sum of n^n/3^n^2, 1:19:03 Q15. Sum of n^n/(n!)^2, 1:22:06 Q16. Sum of nsin(1/n), 1:28:05 Q17. Sum of 1/(n+3^n), 1:32:09 Q18. Sum of sin(2n)/(n+3^n), 1:34:02 Q19. Sum of n((-1)^n)/(3n+1), 1:36:27 Q20. 1/2+1/6+1/12+1/20... 1:38:28 *HELP ME WITH THE REST! THANK YOU* (I will credit you in my pinned comment)
Here are the next 10: Q11. Sum of (1/sqrt(n)-1/n), 58:21 Q12. Sum of 1/n^2ln(n), 1:03:28 Q13. Sum of 1/sqrt(n)e^sqrt(n), 1:06:54 Q14. Sum of n^n/3^n^2, 1:19:03 Q15. Sum of n^n/(n!)^2, 1:22:06 Q16. Sum of nsin(1/n), 1:28:05 Q17. Sum of 1/(n+3^n), 1:32:09 Q18. Sum of sin(2n)/(n+3^n), 1:34:02 Q19. Sum of n((-1)^n)/(3n+1), 1:36:27 Q20. 1/2+1/6+1/12+1/20... 1:38:28
2:26:59 With this kind of series, we can see that 0< 1/n^2 = 1/x, which means it diverges by p test. Since nroot(sin1/x^2) is a greater function, it also diverges. 3:18:00 We can just do the integral test here Here are some easier solutions that I noticed, please correct me if I am wrong. Thank you for this video
Like we cant reduce energy loss to absolutely zero likewise we cant avoid such dislikes but we can supply more energy and use it wisely therefore we must support him always to make those dislikes punny
Dude - you are amazing. I have a tremendous amount of respect for you, especially because I just recently started tutoring students in math (all high school math, undergraduate statistics, and now undergraduate calculus). But my god, man, why would you deprive yourself of food/water for six hours?! My throat hurts just thinking about how much talking is involved in this video!
Thank you so much for your comment. I run marathons and when I train, I will try to run around 10 miles with no food, no water and no stop! So that's the reason! : )
3:17 - I would finish this in 6 hours maybe. 4:03 - Here we start. 6:03:50 - Finishes last question! Goddamn, how can he be so accurate at time assumptions?!?! TRUE MATHEMATICIAN ;) *GREAT WORK*
Thank you for the wonderful videos. After teaching junior high and high school mathematics for 40 years, I retired. My need to understand mathematics has never stopped. So I am attempting to relearn the mathematics that I learned in college (I graduated 52 years ago!!) and forgot since I taught nothing above Algebra 2. I am now 74 and taking Calculus 2 so I really need the help that you provide. Thanks again!!
#BestFriend It was last year when my father was our math teacher in grade 11. I just interrupted him saying: teacher, my father bought me a new calculator yesterday! Then everybody in class started laughing. The teacher (my father) replied: You are so lucky, you have a great dad!
I have this on my exam in a couple days so it is perfect. Thank you very much Steve. Im very grateful for bumping into your channel couple years ago. Every video is so much fun and helpful. 👌😀 Last time I had integrals on my exam and you made a video on 100 integrals...so spot on! Soon i'll be having differencial equations🤟
That’s how I decided I wanted to start studying math🤗 watching videos on UA-cam I didn’t understand but was entertained/interested by. Went back to community college and started taking math classes
2:34:50 1/3 is not less than 0, please do entire video over. Kidding aside, thanks for this epic endeavor, you're the hardest working man in the math world.
these are godsend, i always watch ur 100 [calc2] as prep for my midterms 🙏 for mt1 i watched 100 integrals, now for my second one i am here, studying series! thank you so much for all your work :')
Thank you so much! really super super helpful video! your way to explain the exercises it's so clear and easy, i learned a lot from this video! i just finished the whole 6 hours now, actually it took me several days to finish it, so congratulations for doing the 100 series in 6 hours non stop!
im so glad that you explain almost every step. i think for someone as talented as you, some things might seem "trivial" but for people like me its sooo helpful!
#BestFriend So this happened to me when I was in the 7th grade. My teacher was telling about the shapes and perimeters of different basic shapes like square , rectangle , cube, cone, triangle, etc... A student asked how are they derived. She gave a gr8 explanation for it telling that we take very thin lines of length l and stack them together till the reach the height b and so we get the area to be l*b. It was ammusing. Some years later, when I came to know about calculus , I was amused , that * in essence , she was actually teaching basics of calculus to 13 year olds * ( I know that's an overkill , but can you believe that). It's because of this I love maths (specially calculus) so much . Love your channel You work really hard for this type of content , Keep It Up Love from Indian ♥️🇮🇳🇮🇳
Really impressed with your 100 integrals and 100 series in one take. I really enjoy watching and learning from them. Your videos have reinvigorated my interest in math after 20 years of absence. I would really be impressed and appreciative if you did 100 differential equations. It would be valuable for many students to grasp or recap the whole field.
Really glad that i was able to be taught by this man, hes a very kind, funny and knowledgeable professor. If anyone has the opportunity to choose him as their math professor please do it ! Hes your best bet for any math related classes !
Did this man just say he has haters? Despicable. You keep putting up those absolute value bars my friend, your content is appreciated more then you'll ever know.
So one time in my AP Calculus class, we were doing Khan Academy for integration. I finished early, and then started to watch some bprp to see his “100 integrations video.” My teacher caught me, and decided to see if we could integrate faster than him. We couldn’t beat him. Not even in groups we could do it as fast. #BestFriends
Hi bprp, I just wanted to say thank you for making this video, it helped me so much for my classes. I however, want to mention that at 2:50:00, when doing the telescoping decomposition, you dissmed the 3rd term from the n-1 partial sum, so at the end you would get the 1/2 - 1/2 and 1/4 from the top, and -1/(n+1) + 1/2(n+2) from the bottom, along with the 3rd n-1 term, being 1/2(n+1), which combined with the -1/(n+1) woud give -1/2(n+1). This wouldnt affect the sum as it would still go to 0 when taking the lim as n -> inf, just wanted to make an observation, but regardless, as I mentioned, thank you for this video!!
Thanks a lot blackpenredpen, you've been a great help to me with all your videos. I'm currently taking an intensive course for calc 2, and your video have pretty much saved me all the time. Tomorrow I have my final and I don't need a grade in order to pass. Thanks a bunch and stay awesome.
Thank you, my teacher, Happy Eid Mubarak, and happy new year. Your brother is from Morocco. I watch all your videos. I love mathematics. The way you explain is wonderful. I hope to see you one day. Thank you
Yupp I saw this entire video....from beginning to end solving each problem....this helped me a lot...I have no words to express my gratitude and no words to appreciate your hard work....took me 3 days ...and that explains how much time and effort it takes for an average individual .....might take up the integral challenge next.
#BestFriend I guess my favorite memory in a math class this semester is when I got to teach a whole group of students for a day. So my Honors Math teacher knows I take AP Calculus, so one day he told me to solve the question on the whiteboard. It was a difficult Integration by Parts question but I did it,nevertheless, and he was like “Okay you can continue teaching the class for today.” and I had the best time teaching the students new topics in Calculus they never have heard of. I enjoyed seeing their interest when I showed them some cool stuff concerning series. I guess this experience is so special because i already applies for an Education degree to become a Math teacher, and this experience made me even more excited to teach, and learn math in college.
More maths ... more integrals ... .....without food..no water ...no rest..you are nothing but unstoppable 👏👏👍👍👇👇 And I am really a big fan of you Sir 😀⏰🚩✔⛄100/100
I love your videos and those of Dr. P. The present video is a great review for those taking Calc. II, and for those that studied infinite series a few decades ago. Great short course. Many thanks.
#BestFriend Once in my 8th grade trig. class, a decent friend of mine asked the teacher to use the restroom. The teacher, thinking it was the usual excuse to ditch the class, rejcted his wishes. That was when he told us that he would pee in the recycling bin if our teacher didn't let him leave to go to the restroom. Now, I must add that our 8 grade trig. teacher was a little hard of hearing, so when my friend got up to pee in the recycling bin in front of the whole class, she didn't realize what he was doing for a good 5 seconds. The whole class went berserk after he finished. He got a B- in math that year.
Here you are! You can open a fitness centre and run a course : no food, no water, no stop!
More math, less fat hahaha~
Q1. Sum of 1/n, 4:17
Q2. Sum of 1/ln(n), 11:30
Q3. Sum of 1/ln(n^n), 17:23
Q4. Sum of 1/(ln(n))^ln(n), 23:00
Q5. Sum of (-1)^n/arctan(n), 32:04
Q6. Sum of 2^n/(3^n+n^3), 35:47
Q7. Sum of 3^n/(2^n+n^2), 39:01
Q8. Sum of n*sin^2(n)/(n^3+2), 46:17
Q9. Sum of (-1)^n/sqrt(n+1), 49:31
Q10. 1/2-1/3+2/9-4/27+... 55:31
Q11. Sum of (1/sqrt(n)-1/n), 58:21
Q12. Sum of 1/n^2ln(n), 1:03:28
Q13. Sum of 1/sqrt(n)e^sqrt(n), 1:06:54
Q14. Sum of n^n/3^n^2, 1:19:03
Q15. Sum of n^n/(n!)^2, 1:22:06
Q16. Sum of nsin(1/n), 1:28:05
Q17. Sum of 1/(n+3^n), 1:32:09
Q18. Sum of sin(2n)/(n+3^n), 1:34:02
Q19. Sum of n((-1)^n)/(3n+1), 1:36:27
Q20. 1/2+1/6+1/12+1/20... 1:38:28
Q21. Sum of (n!)/e^(n^2), 1:42:52
Q22. Sum of (n^2 + 1)/(n^3 +1), 1:46:35
Q23. Sum of sin(1/n^2), 1:48:59
Q24. Sum of cos^2(1/n), 1:51:51
Q25. Sum of cos(pi x n)/ln(n), 1:53:33
Q26. Sum of (2n + 1)^n / [n^(2n)], 1:58:09
Q27. Sum of 1/2^[ln(n)], 2:00:35
Q28. Sum of 1/3^[ln(n)], 2:03:23
Q29. Sum of (3n^2 + n)/sqrt(n^5 + 2n + 1), 2:04:16
Q30. Sum of n/(2^n), 2:10:41
Q31. Sum of (n!)^2 / (2n)!, 2:17:43
Q32. Sum of 1 / [n^(1+1/n), 2:21:55
Q33. Sum of 1 / [n^(1 + 1/n^2)],2:26:40
Q34. Sum of 1, 2:30:10
Q35. Sum of n^2 / (2^n + 3^n), 2:30:58
Q36. Sum of (1 - 1/n)^n, 2:35:19
Q37. Sum of (1 - 1/n)^(n^2), 2:36:45
Q38. Sum of 1 / sin^4(n), 2:40:25
Q39. Sum of (n!)/(n^n), 2:41:45
Q40. Sum of 1/(n^3 + 3n^2 + 2n), 2:45:56
Q41. If sum of (an)^2 converges, then sum of an also converge, 2:52:52
Q42. If sum of an converges, then sum of (an)^2 also converges, 2:54:09
Q43. If sum of an converges, then sum of 1/(an) must diverge, 2:55:48
Q44. If sum of an diverges, then sum of 1/an must converge, 2:57:16
Q45. If sum of an converges, then sum of (an)/n must also converge, 2:58:40
Q46. If sum of an and sum of bn both converge, then sum of (an + bn) must converge, 3:00:10
Q47. If sum of an and sum of bn both diverge, then sum of (an - bn) must diverge, 3:01:41
Q48. If sum of an and sum of bn both diverge, then sum of (an x bn) must diverge, 3:03:55
Q49. If sum of an and sum of bn both converge, then sum of (an x bn) must converge, 3:05:57
Q50. Sum of 0, 3:08:15
Q51. Sum of n x sqrt[sin(1/n^2)], 3:08:52
Q52. Sum of [1 - sin(1/n)], 3:12:16
Q53. Sum of [1 - cos(1/n)], 3:18:05
Q54. Sum of 1 / cubert(2^n + 1), 3:22:51
Q55. Sum of 1/[sqrt(n) x ln(n)], 3:25:49
Q56. Sum of (n - 1)/sqrt(n^3 + 2n + 5), 3:26:32
Q57. Sum of [n^2 x 2^(n+2)] / 4^n, 3:32:00
Q58. Sum of [(nth root of 2) - 1], 3:36:55
Q59. Sum of [(nth root of 2) - 1]^n, 3:41:30
Q60. Evaluate sum of an, where a1 = 9 and an = (6 - n) x an-1, 3:43:23
Q61. Sum of [(n!)^n] / [n^(10n)], 3:46:23
Q62. Sum of [(2n)!] / n^n, 3:48:14
Q63. Sum of e^(-n) x sin n, 3:52:46
Q64. Sum of [tan(1/n)] / n^2, 3:56:58
Q65. Sum of (n^10 x 4^n) / n!, 4:01:53
Q66. Sum of (2^n x n!) / (n + 2)!, 4:04:58
Q67. Sum of 1 / sqrt(n!), 4:09:13
Q68. Sum of 1 / ln(n!), 4:11:24
Q69. Sum of [n(n+2)] / (2n+1)^2, 4:15:33
Q70. Sum of [e^(1/n) - e^(1/(n+2))], 4:16:57
Q71. Sum of (ln n) / n^2, 4:21:15
Q72. Sum of n^3 / (2n^5 + 3n - 4), 4:23:32
Q73. Sum of [(1-2n)/(3+4n)]^n, 4:24:54
Q74. Sum of (e^n) / [2^(2n-1)], 4:27:28
Q75. Sum of (n^3 - 2n - 1) / (2n^5 + 3n - 4), 4:30:02
Q76. Sum of 1 / (n + sqrt(n)), 4:33:12
Q77. Sum of 1 / (n x sqrt(n)), 4:35:15
Q78. Sum of sqrt(cos(1/n)), 4:36:10
Q79. Sum of (3^n x n^2) / n!, 4:37:45
Q80. Sum of n / (2^n), 4:41:09
Q81. Values of x for 1^x + 2^x + 3^x + ... + n^x + ... converge, 4:51:19
Q82. Values of x for x^1 + x^2 + x^3 + ... + x^n + ... converge, 4:53:08
Q83. Values of x for sum of (x - 2)^n / n^n converge, 4:54:39
Q84. Values of x for sum of (x^n) / n converge, 4:58:43
Q85. Values of x for sum of (x - 1)^n / (n x 3^n) converge, 5:04:18
Q86. Values of x for sum of (n!) x^n converge, 5:09:00
Q87. Values of x for sum of 1 / [x(ln x)^k] converge, 5:12:24
Q88. Values of x for sum of [1/(1 - x)]^n converge, 5:15:44
Q89. Values of x for sum of (sum of x^m)^n converge, 5:19:35
Q90. Sum of [(-1)^n] / (n!), 5:24:28
Q91. Sum of (pi/2 - arctan n), 5:25:34
Q92. Sum of sin^2 (1/n), 5:29:49
Q93. Sum of 1 / [sqrt n - sqrt(n+1)], 5:32:52
Q94. Sum of [1/sqrt n - 1/sqrt(n+1)], 5:35:55
Q95. Sum of 1 / e^(sqrt n), 5:38:16
Q96. Sum of 1 / [n x sqrt(n^5 - 1)], 5:43:35
Q97. Sum of ln[n/(n+2)], 5:46:12
Q98. Sum of 1/(e^n + 1), 5:49:23
Q99. Sum of 1/ln(e^n - 1), 5:50:42
Q100. 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ..., 5:54:20
Q101. Sum of (3^n x n!) / (n^n), 6:00:25
Mak Vinci omg!! Mak, you are the real MVP!! Thank you!!!
@@blackpenredpen Not at all man, compared to your 6-hour non-stop math doing!
@@VibingMath thx 4 u, and bprp's 6-hour long work. (btw, is he gonna make a playlist called: 100 everything?)
@@蛰扉 Try 100 differentiation series, start from x^100 and differentiate 100 times, will be a lot easier XD
@@VibingMath i was gonna say that! how can u have integrals without derivatives?
School bell: *rings*
Teacher: Let me just say one more thing.
Teacher:
lol😂😂😂
JAJAJJAJAJA
JAJAJAKAJSDNDKSNJZNZKSLDKWINDJX MI PROFE DE FÍSICA
Esto es jodidamente real.
Si
so, what do you eat in the morning ?
me : a bowl of cereals
this guy : a bowl of serials
lol!
Good Joke....☺
@@blackpenredpen 1:12:45 I guess claim is wrong.. put n=4; will not the value be less than 1?
@@blackpenredpen 1:54:08.. if n=1 wont it be infinity leading the series to be divergent?
Dan Cibotaru lmao
That’s a lot of effort bro, those are the people who should be supported ❤
Thank you!
@@blackpenredpen at no.100 the integral of 1/1-x must be -ln(1-x) right? Cause if you differentiate 1/1-x you get 1/(1-x)^2 and what we previously had. Can please check it out and tell me if I'm mistaken?
thanks in advance :)
@@blackpenredpen yeah you smart teacher
Me:**Is absent for one day**
The teacher:
Broooo😂😂😂😂😂😂😂😂😂😂😂😂😂
Tf 🤣🤣🤣
Exactly
🤣🤣😂
Very true
The real talent isn't the math part, it is how he held that microphone for 6 hours easily.
Hahahaha!
that isometric exercise with high volume of 6 hours will give you hypertrophy
Bob Jones oh wow cool 👍
@Bob Jones How can you solve infinitely many problems in a few seconds?
@Bob Jones Gotcha, I thought you were saying you could solve infinitely many specific problems in a few seconds.
I did about 15 of these with my friends in 7th grade, and I was SO TIRED. How you did this without dropping dead is awesome. subbed
7th grade?!
@@danarch1136 he is an Indian and as per my knowledge you should increase his grade by 2 because we all like to fake about our education system
@@giornogiovanna9475 😂😂
@@giornogiovanna9475 you don't get the joke..look at his pfp.. it's fuckin RAMANUJAN ffs. He's referring to him imo
@@Aravind-2906 no he isn't . If this was supposed to be a joke then he would have also changed his name to ramanujan. He is just a 12 yo who wants to look cool.
Her: he's probably cheating on me with other girls.
Him:
Don't ever bring that retarded joke up when learning math while scrolling through the comments.
@@orangehat1924 relax bro damn 🤣
@@KokeBeast23 It was a joke lol
OMAYGHAAAAD im laughing so hard right noww HAHAHAHAHA
🤣🤣
Imagine forgetting to press the record button
Lol
lmao
poor joke smart boy
😂😂🤣🤣
Haha
Just wanted to thank you. Anyone learning math needs to watch you. I've watched so many videos, and was still confused. It wasn't till I found your channel that I understood. Math makes sense!
Someone: What do you watch on UA-cam?
Me: It’s complicated
Lolll
@@blackpenredpen He makes it easy,so you can simply say...wonderful stuff!
I think it is quite easy to answer that question. I would have answered:
"Math"
Do it for 3 years daily and you'll become One Integral Man.
Hope I won't become bald?
@@GiornoYoshikage if you don't get bald you're doing it wrong
@@tutorialeshtmlprod LMFAO OPM
@@vanshajrai6089 One Probability Man ?
@@inflexion7798 xD
I don't understand how i get exhausted after a one hour lecture in my college but left out more energetic after watching this video...Thank you so much for this .
He doesn't love math
Math loves him
Wow! This is such a powerful comment!
true love comes always from both sides...
Oh, sorry, wrong context
@@blackpenredpen Please do more 100 something. Thank You! Big fan!
Too good
Can't be
Math is divine, the only holy thing.
You have to be at least Euler or Gauss for that
@@leonardokeller5254 Were you trying to reference Russian Reversal jokes?
trying to find my homework problem solution in this 6 hour video
ahhaahhaha
@@EdimOmerhodzic-sh6gq still searching
@@mapengbo0314 how bout now?
@@marysued2130 FOUND IT 4:55:02
@@mapengbo0314 lmao
I just watched this during my review for my Calc 2 finals. I understood the how the tests work and how and to what situations they are used through this video more than the notes and lectures in our online zoom classes. Thank you very much. It also was really fun while watching! I hope to see more of this in the future :D
Time stamps for you guys!
Q1. Sum of 1/n, 4:17
Q2. Sum of 1/ln(n), 11:30
Q3. Sum of 1/ln(n^n), 17:23
Q4. Sum of 1/(ln(n))^ln(n), 23:00
Q5. Sum of (-1)^n/arctan(n), 32:04
Q6. Sum of 2^n/(3^n+n^3), 35:47
Q7. Sum of 3^n/(2^n+n^2), 39:01
Q8. Sum of n*sin^2(n)/(n^3+2), 46:17
Q9. Sum of (-1)^n/sqrt(n+1), 49:31
Q10. 1/2-1/3+2/9-4/27+... 55:31
Q10 to Q20. Thanks to "WHY IT"
Q11. Sum of (1/sqrt(n)-1/n), 58:21
Q12. Sum of 1/n^2ln(n), 1:03:28
Q13. Sum of 1/sqrt(n)e^sqrt(n), 1:06:54
Q14. Sum of n^n/3^n^2, 1:19:03
Q15. Sum of n^n/(n!)^2, 1:22:06
Q16. Sum of nsin(1/n), 1:28:05
Q17. Sum of 1/(n+3^n), 1:32:09
Q18. Sum of sin(2n)/(n+3^n), 1:34:02
Q19. Sum of n((-1)^n)/(3n+1), 1:36:27
Q20. 1/2+1/6+1/12+1/20... 1:38:28
*HELP ME WITH THE REST! THANK YOU* (I will credit you in my pinned comment)
Lo hiciste de nuevo :0 asombroso
Here are the next 10:
Q11. Sum of (1/sqrt(n)-1/n), 58:21
Q12. Sum of 1/n^2ln(n), 1:03:28
Q13. Sum of 1/sqrt(n)e^sqrt(n), 1:06:54
Q14. Sum of n^n/3^n^2, 1:19:03
Q15. Sum of n^n/(n!)^2, 1:22:06
Q16. Sum of nsin(1/n), 1:28:05
Q17. Sum of 1/(n+3^n), 1:32:09
Q18. Sum of sin(2n)/(n+3^n), 1:34:02
Q19. Sum of n((-1)^n)/(3n+1), 1:36:27
Q20. 1/2+1/6+1/12+1/20... 1:38:28
@@sPaulish ¿Yo se, verdad?
@@whyit487 Awesome, thank you!!!!
*this had 100 likes before I liked it ironically* 🤯😳🥳
03:45:48 limit conv. against 585. Thank you so much for your effort ❤
What really is impressive is that you keep your smile throughout the whole 6 hours without actually getting tired...
Calc-man💪
Also: 6 hours video 6 ads
Other youtubers: 10 min video infinite ads!
Yep, that's how you win customers in business.
so then the lenght of the video diverges
2:26:59
With this kind of series, we can see that 0< 1/n^2 = 1/x, which means it diverges by p test. Since nroot(sin1/x^2) is a greater function, it also diverges.
3:18:00
We can just do the integral test here
Here are some easier solutions that I noticed, please correct me if I am wrong. Thank you for this video
That 96 dislikes are from the people having no respect for his hard work. It's a shame for them
When someone dislike such a video, it doesn't matter because it's just a sign of mental retardation
Like we cant reduce energy loss to absolutely zero likewise we cant avoid such dislikes but we can supply more energy and use it wisely therefore we must support him always to make those dislikes punny
@@arnavanand8037 or we don't like math 🤷...I can give my opinion like everybody else
It's 548 now. I am worried about the future of this world.
@@Venom-yj7ls That doesn't mean you have to dislike the video! Just ignore it!
Dude - you are amazing. I have a tremendous amount of respect for you, especially because I just recently started tutoring students in math (all high school math, undergraduate statistics, and now undergraduate calculus). But my god, man, why would you deprive yourself of food/water for six hours?! My throat hurts just thinking about how much talking is involved in this video!
Thank you so much for your comment. I run marathons and when I train, I will try to run around 10 miles with no food, no water and no stop! So that's the reason! : )
@@blackpenredpen but you wasnt run at this time you were just teaching us and holding your microphone :)
@@yuanlee3689 two years
@@blackpenredpen whoa didn't know that, nice :)
@@blackpenredpenThanks for This Video .
imagine learning math for 6 hour in school for just one subject.
While you get FREE education on youtube...
Argentine students: 😔
normal situation in korea
Rxckz_школьный курс полностью за не очень много времени? Не удивлён. Не обязательно по одному предмету, есть и другие варианты.
Россия 🇷🇺 Урал.
It’s normal for meh 🤷👀
It's amazing that you got through all of these *_with explanations!_*
: ))))
Thank you!!!! I want to make this useful to all the calc 2 students.
Hahaha, I was like, "You serious, bro?" And then he opened with, "Yes, I'm serious."
chimetimepaprika hahaha yes, I am serious!
Your humor throughout the video made these series tolerable. Thank you.
Yo this dude was flexing his pokeball for 6 hours straight. Whatta legend
DiehardTheTryhard thank you!!
😂
its a magic 8 ball uncultured swine
while how else is he going to catch all the integrals
Mom : i have a small work for u at home son.
Work at home : .....
Vaibhav Agarwal Lol
Omg I am so thankful for this channel, 100 guided work along practice problems?? This is gonna be so helpful for my test on friday.
3:17 - I would finish this in 6 hours maybe.
4:03 - Here we start.
6:03:50 - Finishes last question!
Goddamn, how can he be so accurate at time assumptions?!?! TRUE MATHEMATICIAN ;)
*GREAT WORK*
LOL!! I don't know how either!! : )))))
Wow....
@@blackpenredpen Here's Probability literally ....i think.
This man is unstoppable. He will only quit once he stumbles upon the solution that merges general relativity and quantum mechanics.
Scott Maday thanks!
That’s tai Lopez!
Thank you for the wonderful videos. After teaching junior high and high school mathematics for 40 years, I retired. My need to understand mathematics has never stopped. So I am attempting to relearn the mathematics that I learned in college (I graduated 52 years ago!!) and forgot since I taught nothing above Algebra 2. I am now 74 and taking Calculus 2 so I really need the help that you provide. Thanks again!!
Just took my cal 2 final. Really makes me appreciate what you’re doing. You are a trooper keep it up my guy
Glad to hear!!!
#BestFriend
It was last year when my father was our math teacher in grade 11. I just interrupted him saying: teacher, my father bought me a new calculator yesterday! Then everybody in class started laughing. The teacher (my father) replied: You are so lucky, you have a great dad!
Awww : ))))
Beast mode! I wish you were my Calc 1 teacher. 35 yr old returning to school and you are helping get through it. Thank you very much
1:09:30 blackpenredpen.exe has stopped working
thats why i came thx
Eventually, he stopped thinking
U r legend
@@GiornoYoshikage what a man of culture we have
bprp.exe not working
Seriesly awesome!!!! 😄 And awwwww, thanks for the shoutout ❤️
HAHAHAHAHAH
Dr. Peyam Yeah! He led me to your channel a few months ago! Now I'm subscribed to both of you! (Great pun, by the way)
whoa~!
Why It? I didn’t realize you were not Justin Y at first and I was like Justin Y watches call videos.
Seriesly the best comment
his videos made me solve integrals and series in my free time
👍
I have this on my exam in a couple days so it is perfect. Thank you very much Steve. Im very grateful for bumping into your channel couple years ago. Every video is so much fun and helpful. 👌😀
Last time I had integrals on my exam and you made a video on 100 integrals...so spot on! Soon i'll be having differencial equations🤟
Mihailo Opacic
I thought about that... but 100 DE will prob take 10 hours
I'm just now studying linear algebra, it has helped me a lot to learn the criteria and how to use them. Good job
I just finished doing all of them alongside you. Love you Mr. blackpenredpen
I understand none of this yet am still thoroughly entertained.
That’s how I decided I wanted to start studying math🤗 watching videos on UA-cam I didn’t understand but was entertained/interested by. Went back to community college and started taking math classes
@@cassied9327 nice 🙂😊
2:34:50 1/3 is not less than 0, please do entire video over.
Kidding aside, thanks for this epic endeavor, you're the hardest working man in the math world.
Haha i think he meant it was less than 1
Less than 1
@@sses1894 Joke went over both of your heads.
😀😀😀 le mje .kaache kaat
@Ice Wizard Sure did.
these are godsend, i always watch ur 100 [calc2] as prep for my midterms 🙏 for mt1 i watched 100 integrals, now for my second one i am here, studying series! thank you so much for all your work :')
Thank you so much! really super super helpful video! your way to explain the exercises it's so clear and easy, i learned a lot from this video!
i just finished the whole 6 hours now, actually it took me several days to finish it, so congratulations for doing the 100 series in 6 hours non stop!
You're welcome! Great job to you as well!!!
im so glad that you explain almost every step. i think for someone as talented as you, some things might seem "trivial" but for people like me its sooo helpful!
I am glad to hear so! thank you!!!
@@blackpenredpen hey! I would like to hear about you, do you have studies? I Guess yess, but your personal Life! Tell us
1:34:37 That joke caught me so off guard, you really do enjoy making these videos, I can tell!
#BestFriend
So this happened to me when I was in the 7th grade. My teacher was telling about the shapes and perimeters of different basic shapes like square , rectangle , cube, cone, triangle, etc...
A student asked how are they derived.
She gave a gr8 explanation for it telling that we take very thin lines of length l and stack them together till the reach the height b and so we get the area to be l*b.
It was ammusing.
Some years later, when I came to know about calculus , I was amused , that * in essence , she was actually teaching basics of calculus to 13 year olds * ( I know that's an overkill , but can you believe that). It's because of this I love maths (specially calculus) so much .
Love your channel
You work really hard for this type of content , Keep It Up
Love from Indian ♥️🇮🇳🇮🇳
Wow and thank you!!
Bro can u explain how your teacher was actually teaching basics of calculus through that example? Don't get me wrong. I am just curious.
Come on dude do us some videos .. ineeed maaatth
Are you a robot!?🙂
Sir, you are just a true example of dedication,supervision and perseverence!!
❤️ From INDIA
Thanks!
Really impressed with your 100 integrals and 100 series in one take. I really enjoy watching and learning from them. Your videos have reinvigorated my interest in math after 20 years of absence. I would really be impressed and appreciative if you did 100 differential equations. It would be valuable for many students to grasp or recap the whole field.
Peter Kastrup-Misir thank you!!! 100 differential equations... hmmmm...!
Peter Kastrup-Misir,
Or instead of 10^2 maybe 2^5 equations.
1:48:59 for number 23, you can say that for all positive x values sin(x)
Didn't have to leave your channel once to study for my cal 2 test. Thank you!
best way to study for a final, thanks for the video! Hopefully something similar appears on my final!
YOU ARE THE BEST PERSON I HAVE EVER KNOWN.
i didnt start watching the video but i sincerely thank you for your hard work, thank you for helping us ❤
Bro please do continue making videos in your 100 series...... They Are just something more than amazing.
And your accent is very pleasing..... 😁
Really glad that i was able to be taught by this man, hes a very kind, funny and knowledgeable professor. If anyone has the opportunity to choose him as their math professor please do it ! Hes your best bet for any math related classes !
Gustavo Torres heyyy thank you Gustavo!
blackpenredpen no problem professor 🙂✌🏽
Did this man just say he has haters? Despicable. You keep putting up those absolute value bars my friend, your content is appreciated more then you'll ever know.
So one time in my AP Calculus class, we were doing Khan Academy for integration. I finished early, and then started to watch some bprp to see his “100 integrations video.” My teacher caught me, and decided to see if we could integrate faster than him. We couldn’t beat him. Not even in groups we could do it as fast. #BestFriends
Any person records over 3 hours.
*Comments:* Imagine if he/she forgot to press record button.
Did the 6hours to study for a test. Now i feel so confident, thank you so much
Hi bprp, I just wanted to say thank you for making this video, it helped me so much for my classes. I however, want to mention that at 2:50:00, when doing the telescoping decomposition, you dissmed the 3rd term from the n-1 partial sum, so at the end you would get the 1/2 - 1/2 and 1/4 from the top, and -1/(n+1) + 1/2(n+2) from the bottom, along with the 3rd n-1 term, being 1/2(n+1), which combined with the -1/(n+1) woud give -1/2(n+1). This wouldnt affect the sum as it would still go to 0 when taking the lim as n -> inf, just wanted to make an observation, but regardless, as I mentioned, thank you for this video!!
This is how I will study for my Calculus BC AP test next Tuesday. Just an hour a day.
nice!!!
Lmao good luck 👍
I'm watching the full 6 hours with pausing to prepare for Analysis 1. This video is pure gold :)
Just took my Calc 2 final yesterday! wish me luck🙏
Anthony M best of luck!
Thanks a lot blackpenredpen, you've been a great help to me with all your videos. I'm currently taking an intensive course for calc 2, and your video have pretty much saved me all the time. Tomorrow I have my final and I don't need a grade in order to pass. Thanks a bunch and stay awesome.
Thank you, my teacher, Happy Eid Mubarak, and happy new year. Your brother is from Morocco. I watch all your videos. I love mathematics. The way you explain is wonderful. I hope to see you one day. Thank you
I hope you win the Nobel Price in the future ! You are the best teacher !
lmao I am embarrassed and ashamed I came here thinking this was some type of Netflix challenge. Now if you'll excuse me...
i thought the same lol
😂😂😂😂😂
😂 I’m dying. You came for the Netflix, did you stay for the math?
Lmao
You 're one of the best teachers who I 've ever seen. I 've also subscribed your channel. Love from Bangladesh 🇧🇩🇧🇩🇧🇩🇧🇩🇧🇩🇧🇩
@S H A K I B You 🥰🤪🥰🥰🥰🥰
Damn breaking records left and right! Keep it up! Your channel will be legendary among the Maths Channel on UA-cam
Jalu Reswara hahaha thanks!!
Okay....I know I shouldn't say this cuz I think you're crazy enough to actually do it, but 100 differential equations.
You guys gonna kill him with that
Nonlinear PDE's.
100 single-digit addition problems
@@orcishh You're Orcishist
Differential equations is literally easier than series. BRuh/OOAf
Thankssss for putting effort and time to explain these for students in need. You deserve the worldddddd. God bless youuuu
Happy to help!
me: i'll go to sleep early this time
youtube algorithm: NO
This is one of the greatest youtube mathematicians on youtube
Thank you very much, you are a very wonderful person who provides an amazing way of explaining to you a thousand greetings from Algeria
La campana de la escuela: suena
El profesor: esperen, una cosa más.
El profe:
XD
Yupp I saw this entire video....from beginning to end solving each problem....this helped me a lot...I have no words to express my gratitude and no words to appreciate your hard work....took me 3 days ...and that explains how much time and effort it takes for an average individual .....might take up the integral challenge next.
OMG your videos have saved me from my Calculus II class. I just passed my calculus exams with ease. THANK U SO MUCH!
#BestFriend I guess my favorite memory in a math class this semester is when I got to teach a whole group of students for a day. So my Honors Math teacher knows I take AP Calculus, so one day he told me to solve the question on the whiteboard. It was a difficult Integration by Parts question but I did it,nevertheless, and he was like “Okay you can continue teaching the class for today.” and I had the best time teaching the students new topics in Calculus they never have heard of. I enjoyed seeing their interest when I showed them some cool stuff concerning series. I guess this experience is so special because i already applies for an Education degree to become a Math teacher, and this experience made me even more excited to teach, and learn math in college.
Oh wow, very nice!
Ok UA-cam Recommendations, I will watch some random guy calculating for 6 hours straight,
Finally I've got my Favourite derivative series by searching on UA-cam from BD🇧🇩💓💓😊
More maths ... more integrals ... .....without food..no water ...no rest..you are nothing but unstoppable 👏👏👍👍👇👇
And I am really a big fan of you Sir 😀⏰🚩✔⛄100/100
I love your videos and those of Dr. P. The present video is a great review for those taking Calc. II, and for those that studied infinite series a few decades ago. Great short course. Many thanks.
dude you're so good, appreciate your hard work and help!
Glad to help!
this is incredibly impressive! how long did it take for you to prepare for this?
hope you feel better lars ❤︎ congrats chester!
A very long time.
Did I just watch a 6 hour lecture on calculus even though I have no clue what’s going on? Yes, yes I did.
I've got a Calc Two summer Session A final coming up and you are a life saver. Thank you for what you do!
when u enjoy what u do you will not remember time
very true!!!!
Excellent explanations ❤
I'm studying physics and this is gold
I don't know shit of what's going on, but his passion made me watch the video. It's so entertaining!
He needs credit for holding on to that bal- microphone* the entire time
9:41 PM
6/20/2019
Happy John fo sho!
@@blackpenredpen ♥️
7:54 AM
6/22/2019
11k BTC
@@happyjohn1656 why does it say time
2:18 AM
11/2/2020
@@MinecraftPlayer-tl5lx lol watching in lockdown again
6:18Am
5/11/2020
@@sunilparekh4581 Are you writing the time manually?
when you sleep a half of lesson and than wake up in the middle of it and dont understand a thing
How about Sum of (1
1 ad per hour, perfectly balanced as all things should be
#BestFriend Once in my 8th grade trig. class, a decent friend of mine asked the teacher to use the restroom. The teacher, thinking it was the usual excuse to ditch the class, rejcted his wishes. That was when he told us that he would pee in the recycling bin if our teacher didn't let him leave to go to the restroom.
Now, I must add that our 8 grade trig. teacher was a little hard of hearing, so when my friend got up to pee in the recycling bin in front of the whole class, she didn't realize what he was doing for a good 5 seconds. The whole class went berserk after he finished.
He got a B- in math that year.
I have a calc 2 test on series in about a month. Going to rewatch this video multiple times until I understand every problem by heart
Try my “all-in-one” calculus problem 👉 ua-cam.com/video/3s1WYUWYEKU/v-deo.html
thn8u7 xl0