Calculus 2 - Geometric Series, P-Series, Ratio Test, Root Test, Alternating Series, Integral Test
Вставка
- Опубліковано 7 лют 2025
- This calculus 2 video provides a basic review into the convergence and divergence of a series. It contains plenty of examples and practice problems.
Integral Test For Divergence: • Calculus 2 - Integral ...
Remainder Estimate - Integral Test:
• Remainder Estimate For...
P-Series:
• P-series
Direct Comparison Test:
• Direct Comparison Test...
Limit Comparison Test:
• Limit Comparison Test
_________________________________
Alternating Series Test:
• Alternating Series Test
Alternate Series Estimation Theorem:
• Alternate Series Estim...
Absolute & Conditional Convergence:
• Absolute Convergence, ...
The Ratio Test:
• Ratio Test
The Root Test:
• Root Test
__________________________________
Series Tests - Practice Problems:
• Calculus 2 - Geometric...
Taylor & Maclaurin Polynomials:
• Taylor Polynomials & M...
Taylor's Remainder Theorem:
• Taylor's Remainder The...
Power Series - Interval Convergence:
• Power Series - Finding...
Power Series - Derivatives & Integrals:
• Power Series - Differe...
___________________________________
Calculus Final Exam and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections
Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
Next Video: ua-cam.com/video/urPIxvNBXF0/v-deo.html
Thanks for this!
HOW DOES THIS MAN KNOW EVERY SINGLE PIECE OF INFORMATION ON THE PLANET?! You are a lifesaver I swear to god if I was not broke, I would donate at least 10 grand coz your lectures are better than every other class I was ever in. You should run for president
@@ahmedmohamedaligalal9165 Ahh yes, allah
@@ahmedmohamedaligalal9165 u right tho xDDDD
i dont mean to be so offtopic but does anybody know a trick to log back into an instagram account..?
I was stupid forgot my password. I love any tips you can give me!
@Aarav Raylan i really appreciate your reply. I got to the site on google and I'm in the hacking process atm.
I see it takes a while so I will reply here later when my account password hopefully is recovered.
@Aarav Raylan it worked and I actually got access to my account again. I am so happy:D
Thank you so much you saved my account :D
bro Imma have a maths test in 2 hours.. prof made all these incredibly convoluted.. I absolutely love the straightforward manner you built up this video. it is incredible that some people can sum up months of curriculum in 45 minutes and everything is clear, all seems easy and meaningful in contrast to endless lessons in uncomfortable chairs
mad respect
This is more like 1.5 weeks or so
howd you do?
Tbf tho actually learning the content vs memorizing the formulas are completely different. As a review tool, this is great but if you get asked a single out-of-the-box question that requires deep knowledge of the topic then just knowing a bunch of formulas isn't gonna give you the intuition to actually unpack any of this. I'm self-studying for BC and I find it helps a lot to watch these vids in tandem with another explanatory resource like Pauls Online or Khan Academy, which usually have intuitive explanations or proofs of each concept.
@@lambda5949 but it means nothing to me whether I memorize the formula or understand the formula, I just need a pass in order to continue my university study which is nothing about maths. It is just silly that my school make maths compulsory even for the history major.
@@dhuka4969 Oh yeah, in that case, this vid makes sense, didn't think universities required that kinda thing so I was assuming this vid was tailored for high schoolers.
1. Divergence Test: 0:21
2. Geometric Series Test: 0:58
3. P-Series Test: 1:51
4. Telescoping Series: 2:33
5. Integral Test: 5:01
6. Ratio Test: 6:12
7. Root Test: 7:14
8. Direct Comparison Test: 8:12
9. Limit Comparison Test: 8:59
10. Alternating Series Test: 10:28
11. Absolute Convergence AND Conditional Convergence: 11:26
12. Practice Problems: 12:41
goat
Love u
You are so sexy.
Bro the best
I really appreciate this. I'm trying to focus on reviewing the ones I suck at, so this really helps me skip the stuff I'm already comfortable with.
Why have I looked everywhere in my book, the recorded lectures, other math books, etc. to find a list of the tests and how/when to use them, and this is the only resource I've seen that actually goes through them. You are truly God's gift to students, sir.
I just want to say thank you so much. I watched a bunch of your videos on Calc 2 and I just aced my second exam. 100/100. Thank you so much you have no idea how much you truly help people.
You explained 43 minutes, that's already like 3 weeks of calculus II all in 1 video! Thank you so much man!
We covered this topic within half an hour in our university🥲
@@nipuniherath1451 you covered 11 topics in half an hour??? u need a new university bro. that makes no sense. maybe 30min-1hr for each topic but not 30 min for all 11 lol.
@@Maxim-Clutch-papi Yeah we did all of these with sequences in one lecture
@@nipuniherath1451 30 minutes??? This is like 20% of all the content for calc 2
@@benjaminwhitehead4050 Over here at UT it's the same case lol they treat calc 2 as a weed-out class
I cannot put into words how much this channel has gotten me through college. My man you are an absolute legend!
Same!
Thanks! You saved my life for calculus I have an exam comming up and u really summed it up well :)
my calculus 2 final is in exactly 12 hours and before I started watching your videos 2 hours ago, I had absolutely no idea what this wizard scripture is
But now I can safely say that I actually understand it and I'm going to ace the exam tomorrow
I can't thank you enough, you are my hero /:
how did you do
how did you do
@@vaiterius he died
@@axlrose5082 its safe to say, yes he died
@@diags_1109 Res in peace
i am retaking calculus two because of this chapter, and I am currently relearning it and still barely getting it but this video is saving my life tbh !!!
so how did it go?
It was so bad they died on the spot. Rest in Peace Jaz
@@greypoint000 let's have a moment of silence for Jaz
I had to retake it as well, I’m passing with a 90% now!
SchmidtyBangBang Me too! Glad I’m not the only one who is retaking it and smashing the course lmao
I watched this video 4 hrs before my calculus exam and I understood all about the tests in 43:51 minutes #wow.....My lecturer spent 4 weeks on this topic and I didn't get anything LOL.....You the best bro
your ability to make multiple high level topics so easy to understand is out of this world, you're awesome.
This is my second Academic year in Engineering,,you have always been my reference ever since I started. As I comment on this page today, there is an examination I must sit in a few hours !! Good work and Thank you Sir.
I have a calc ii exam in two hours, this video and your channel in general has been a life saver. Before I found your videos I failed my first quiz (50%, mean score being 53%), and after finding your channel I managed to a much better score on my second quiz (85%, mean score being 54%). Thanks to you I can be confident I'll score at least an 80, and even hope for a 90. Honestly i would be failing without your channel.
In my uni it’s called calculus 3 whyy
Who else got a calc exam coming up?
Me😁
@@vijaynagalla3989 me
Me 😂
in 2 days :0000
Me and series had never been my strong topic😅
I have a math test coming up in two days and you just summed up 3 weeks worth of notes into a 45 min video!
a video that's less than an hour has tought me more stuff than my professor did in a week
My calc 2 final is tomorrow and I'm here trying to retain as much information as I can, watching your videos. Thank you, you're a life saver
Simply the GOAT. Greatest UA-cam video I’ve ever watched from an educational perspective. Organic chemistry tutor I love you
We must protect this man at all costs! Bro just saved me an hour before my exam, and I will forever be thankful!!!!
I wanna say thank you. This video is so helpful. I got 96/100 in my third exam
Bro you're the saviour of all engineers.
All hail O-Chem Tutor
These video's are fantastic! I am so thankful that you made these, my cal2 teacher is horrible and you are saving my college career with these.
You have a gift for being able to condense a lot of information into one video and have the viewer leave with a good working understanding of the topic. You are the best math youtuber in this regard! Thank you!
yall are lucky to have these in calc 2, i have these in my calc 1 exam in 3 days
The Organic Chemistry Tutor once gave a student private lecture.The student is known as Stephen Hawking nowadays.
he ded now
Are you turkish?
was
Professor Organic Chemistry Tutor, thank you for a monster review of the different tests for Convergence and Divergence in Calculus Two. This is a tremendous amount of material for a student to absorb in Mathematics. The old fashion way to learn any subject is practice and pattern recognition. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.
Got a BC calc AP in 9 hours and not once did I ever understand how to do these, let’s goooo
My calculus final resulted this day, and I probably got 30-40 point by watching this video on the night of the day before the exam. Thanks man. Even though my math is good, I was confused by many tests in series topic. Great explanation video without confusing parts.
Who disliked this? This is so nice and concise, with practice problems to boot. Perfect.
I got a 100% on my calc 2 final. Thank you with every ounce of sleep that I was deprived of. You deserve it😭😭
Hell yeah! This video is saving me. Thank you so much for making this! My teacher spent 10 days covering this material, but I did not understand. Watched your video and now I'm ready for the exam.
One of these days I am about to beat up that "That tutor guy" ad dude. LIKE STOP IT MAN let me just learn in peace. I AM NOT TIRED OF SCOUNGING UA-cam FOR MATH HELP. My boi organic Chem Tutor got me covered.
This man deserves the Nobel peace prize because he probably prevented so many violent outbursts from STEM major students.
This is a lifesaver you have no idea how much I was struggling - I have to take an exam in a couple hours and I feel at least mildly confident in my ability to get a passing grade now. Thank you so much!!!
Yo Organic Chemistry tutor thank you for your videos, I have a barrier with my teacher and have been struggling in my class. But thanks to you and hours of practice I feel more competent in the subject. I'm sure you get this enough already but thank you for your time and dedication to helping us students out.
This Man is a life saver. I am in the first semester of my university, and have a calculus exam coming up. Since I unfortunately contracted covid during this sem, i was unable to study properly. This Man literally summed up an entire chapter which my teacher taught in 3 weeks, in LESS THAN AN HOUR! And i literally feel so confident after this. Man, you are so special! I wish I had a teacher like you!
Thank you. I love you so much. Calculus is not that hard we just need the professors to teach the same way you do.
At 30:52, I really like the way you said "excuse me" . I realised, at least the man whom I am learning with is not a robot.
Currently learning Calculus right now and this is a lifesaver. Thank you!!
watching this 1hour before my exam 💀
How did you exam go?
@@Microwave342 I passed lol 😂
Thanks for asking ;)
@@realndu did u ever study before watching the video
@@saifkharadi3010 Yeah yeah I did. But I usually leave the Topic of Series last. Hence I did it last minute.
Ong, I owe my degree to you, an absolute GOAT! This video was literally the reason I got a 93% on a 50% avg sequences and series exam!
Speed at 1.75, binge watch and practice through James stewart calculus .. All the best lad for your finals!
How did that work out for you?
@@aurelionsol5134 I got a B minus. That's fantastic, particularly because I'm pursuing my bachelor's degree part-time.
I believe the integral questions are the part where I made the most mistakes. In tutorials, the questions given are single problem like u-sub, integration by parts or integration by partial fractions. Just one of each and never a mix of those.
But my examination will have an integral question that needs to be solved by u-sub and integration by parts or u-sub and partial fractions, etc.
just wanna let you know, youre the best. been watching your videos since highschool whenever i dont understand my teachers
thank you for taking the time of day to make these videos! I don't know how I would get by without you and your videos!
UA-cam must deliver US 100, 000, 000 because this man is a HUMANITY SAVIOR....freeing us from ignorance, freeing us from fear to mathematics. EEEEEEXCELLENT JOB!!
Wow! 2 weeks of material condensed into a 44 min video. Thank you so much!
I dont know how to thank you. I understood these concepts, thank you so much, god bless you!!
WOW! Complete, accurate, precise, I found my new online math teacher. Amazing Content!
I love this guy! I don’t see many people in the comments actually saying how beautiful these math “tests” are that mathematics has a whole sorta new number series that can prove vital things in an equation.
I love the asmr qualities of his videos, his voice, his writing, the lil clicks especially
This person is singlehandedly saving my calc 2 grade T-T
Pray for me boys, it’s 2 am and this calc test determines if I pass or bot
Did you pass?
@@rachelpark4992 yes
@@ClimberWithoutTheBcongrats
@@rachelpark4992 ended up flunking outa the program anyway 💀
Thanks!
best video ever in the history of youtube imo ngl
Got a calc 2 final tomorrow at 2 and you're a life saver!!
Imagine paying for Prep101 when u have this guy
Next Video: ua-cam.com/video/urPIxvNBXF0/v-deo.html. Next Video: ua-cam.com/video/urPIxvNBXF0/v-deo.html.
my friend and i were screwed but this taught us more in one sitting than we learned in class or after days of reviewing notes. thank you i think you just saved us on this test
LOL I have a test this Tuesday. Good timing GOAT
same
wtf me too
you are so professional. you are better than my doctor lol.. thanks man.. god bless you ! I hope that you can achieve what you want to achieve in your life.
edit:you gained a new subscriber ..you are a legend!
i swear that if i didn't know you, i wouldn't understand calculus lessons. now, I can learn well than ever.
Gracias profesor, es usted un hombre increible, teengo un examen en 6 horas, recen un ave maria por mi, quiero vacaciones.
Un saludo desde madrid
Currently watching this 2 hours before my calc exam. Let's hope this works.
it wont
What did you get?
Suprsingly a 98%, thank you
@@dylanholman2000 you give me hope...thank you so much beautiful person.
give this man his honorary phD at this point
Exam in 14 minutes it’s been good boys 🫡
You just summarized 1 month of lectures in 43 minutes and 51 seconds and did a better job at it too
When I get my bachelors and get a high paying job I’ll donate a portion of my first pay to this channel as a thanks
Who else is watching review videos before their exam on this? Life saver this man is.
19:25 lim n-> inf = 0, he said passes divergent test. I thought he just discussed that a series will diverge if the lim -> inf =/ 0. Yet, his example here claims it approaching 0 passes the divergent test? I am confused
edit: It's late. I see my error. "pass the divergence test" does not mean we want the series to specifically diverge. In an alternating series we WANT the lim -> inf = 0 so it *passes* the divergence test i.e. we can continue to prove the convergence of a series continung with the alternating series test by checking the next term is less than or equal to the previous term.
16:02 geometric series
17:59 alternating series
22:04 telescoping series - partial fractions
29:26
good luck on the AP test tomorrow
It's currently 2:26 a.m, where i'm living,i've been binging your youtube channel because it's finals week . My test is in about 7 hours . Im lacking sleep AND information . Send help SOS.
literally just saved my life... i can't wait to donate once i have my degree!
i have exam tommorow after 12 hour , this saved me
thanks for making these amazing courses !
I Passed the exam
if math god existed it would be this man. For every math topic I encountered he already made a video about.
You are a great teacher . Your teaching methodology is very simple and easy to learn. You are doing a great job for a lot of people........
this series has helped me a lot with my examns, however the part where you are calculating de limit of certain things can be easier by just taking the coefficient of the unkown X with the highest exponential
Kindly bring up more challenging examples to solve for us cos our lecturers aren't having mercy on us in our exams
This video deserves +100M views
Thank you for this video, I went from barely knowing anything to knowing all I needed to know within like 8 hours of cramming
Me fr lol, I spent all day just watching this video on repeat and taking notes cuz I procrastinated all my studying, now I feel ready lol
this is one of the best videos i have ever seen...
Thank You. Best math help UA-cam channel out there
Wooo. Cramming for Calculus BC Exam tomorrow :)
Good luck!
Thanks for your help. This really helped me with AP Calculus BC
I think the problem at 37:31, we can use direct comparison test instead of limit comparison test since the bn is larger than an already
Almost 2 fucking moths in class to cover all this and I did understood shit from my professor. And you made this so easy to understand Thank you, I am 4 years late to this video and the video is still saving college students thank you.
You're an absolute god-send. Thanks for helping us get through school/uni XD
literally your the only way I was ever able to pass calculas 2
Bro if I ever hit the lottery I’m giving 10% of my total winning to you. You’re the closest thing our world has to a modern day Jesus.
You're never going to hit the lottery and you're certainly not giving him 10%.
@@jameskennedy674 arent u fun
Calc exam in 3 days. I’m gonna watch so many of this man’s videos lmao
I’m going to ace this test tomorrow, all because of you. Goat
You are the best bro you just saved my life
bro knows everything
You're such a life saver
For the example at 35:58, could you also use the direct comparison test to show that the series is convergent?
That's what I was thinking too, cuz the LCT seemed unnecessary when you can just see Bn > An, Bn converges, so An converges.
You truly are a hero, I cannot express how thankful I am :'')
Yo studying last min for a important calc test was panicking until I found this review video. Also Duke Bozikowski thanks bro for the time stamps you're the real Life saver in combo wtih the Organic chem teach
my hands are partially frozen and Im typing fast so forgive my grammar mistakes
ayo we all gonna ace our exams now cause of you, thanks for the help you absolute legend!!!