Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: ua-cam.com/video/tHy3TXmZpF0/v-deo.html
I remember watching your videos before the January 2020 algebra regents exams and they have helped me a ton. You are one of the main reasons why I passed. My teachers would never explain things to me the way you do. You make everything seem like a piece of cake compared to my teachers. Just wanted to give you a big thanks.
Followed u for a long time now, thank you for helping my calculus, my Ap physics, my chemistry 12. And now even helping me when I am in uni now. You are a true lad, and deserve the sub. Thank you again for helping me get into Imperial college.
You're amazing and I love you. Thank you so much for everything you do!!!!! I have used you for Organic Chemistry, Calculus 1, Calculus 2, Physics 1, and Physics 2.
Professor Organic Chemistry Tutor, thank you for using multiple well-known examples to explain/analyze Converging and Diverging Sequences in Calculus Two. In all Calculus textbooks, there is a whole chapter on Sequences and Series. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.
I have been stuck on Sequences and Series for three days now. I don’t understand it, but your videos cleared it up a bit. I really hope the next bit of your videos help because I don’t have any other ideas.
@@FerghusCameron Just to take the n to an easier place. This can be solved by many ways, and you can keep the n and evaluate it to find the answer (if it's converging or diverging) but dividing by 1/n takes the n to 5/n which leads to the final answer easily (because of the rule 1/n=0).
@@FerghusCameronif you took the limit as n approaches infinity, you’d end up with infinity over infinity. By multiplying by the numerator and denominator by 1/n, you are able solve. Another method of solving for the infinity/infinity problem is applying L’Hopital’s Rule, which would also give you the same answer and is more applicable in vague situations where multiplying by 1/n isn’t available or intuitive.
for anyone else scratching there head at this! plugging in inf into (1+1/n)^n = (1+1/inf)^inf = (1+0)^inf = (1)^inf = 1^inf = undefined this is why we had to solve it
why do u use l'hopital rule insted of just substitute infinity in the equation lim n-> infinity n * sin(1/n)??? and all your video are just unreal. u made life easy for us.
why would you add the last step at 22:15? 1/(n+2) is just 1/infinity which is zero. Absolutely no need to multiply top and bottom to get the zero in the numerator
I'm lost at 19:08. Apparently the answer is now 1, but why couldn't it be 0? sin(1/n) would return 0 and anything multiplied by 0 is 0. Why is that invalid? Are we only able to find the sequence when n only appears once in the function?
Never mind i understand now. The sin of 1/n may approach zero but it never reaches zero. Then it is multiplied by what ever n is as it approaches infinity.
At 13:49, why can you determine it's convergent since lim is 0 here? The divergence test on our slide said that you can't determine whether it's convergent or divergent straight forward if lim=0. I'm so confused:(((
I think you're getting confused between the convergence and divergence of series and of sequences, the divergence test of series needs the limit you're talking about, and in this example we can't determine whether the infinite sum is convergent or divergent(the series) but what we can determine in this example is that the sequence will end up at 0 when we approach infinity
Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
Next Video: ua-cam.com/video/tHy3TXmZpF0/v-deo.html
You literally have the best Calc II tutorials. It’s great learning material for everything in the course. You have a good knack for explaining things.
Which is ironic, organic chem tutor lol
learning this in pre calc lol
I am watching it 2hrs before exam😅
its actually not ironic at all. ANY stem or applied stem besides undergrad general bio requires strong math @@zeldasama
thats calc1
I remember watching your videos before the January 2020 algebra regents exams and they have helped me a ton. You are one of the main reasons why I passed. My teachers would never explain things to me the way you do. You make everything seem like a piece of cake compared to my teachers. Just wanted to give you a big thanks.
The world would have fewer engineers without you, life saver.
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thank youuu
Followed u for a long time now, thank you for helping my calculus, my Ap physics, my chemistry 12. And now even helping me when I am in uni now. You are a true lad, and deserve the sub. Thank you again for helping me get into Imperial college.
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Nursultan Beloved this is only the first section in the first chapter in my course and at most only one question will come on it in the test.
@@theadel8591 I feel like that'll be the case for us, except I bet most of it is going to be power series
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I watched several videos explaining convergent and divergent but only this video makes me fully understand the concept. Kudos and thank you
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Watching this 12 hours before my final
same
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He is much better than some intelligent professors at the colleges in the way he explains materials.
Professor Organic Chemistry Tutor, thank you for using multiple well-known examples to explain/analyze Converging and Diverging Sequences in Calculus Two. In all Calculus textbooks, there is a whole chapter on Sequences and Series. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.
you're making it really fun to learn math and really well made course
you basically explained 4 weeks of college in 1 video
love your style of teaching and your voice, thank you for saving my life
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Same here
Yes it is cause the lim as n>infinity of ln(1+(1/n))/(1/n) is ln(1+0)/(0) which is undefined.
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I have been stuck on Sequences and Series for three days now. I don’t understand it, but your videos cleared it up a bit. I really hope the next bit of your videos help because I don’t have any other ideas.
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At 4:30 why do you multiply the top and bottom by 1/n? How do I recognize when to use this?
Did you find out the reason? I just started Pre calculus and would like to know thr proof for multiplying the top and bottom by 1/2
@@FerghusCameron
Just to take the n to an easier place. This can be solved by many ways, and you can keep the n and evaluate it to find the answer (if it's converging or diverging) but dividing by 1/n takes the n to 5/n which leads to the final answer easily (because of the rule 1/n=0).
@@FerghusCameronif you took the limit as n approaches infinity, you’d end up with infinity over infinity. By multiplying by the numerator and denominator by 1/n, you are able solve. Another method of solving for the infinity/infinity problem is applying L’Hopital’s Rule, which would also give you the same answer and is more applicable in vague situations where multiplying by 1/n isn’t available or intuitive.
Thank you sir for clearance this topic sir.........From India
for anyone else scratching there head at this!
plugging in inf into (1+1/n)^n = (1+1/inf)^inf = (1+0)^inf = (1)^inf = 1^inf = undefined
this is why we had to solve it
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why do u use l'hopital rule insted of just substitute infinity in the equation lim n-> infinity n * sin(1/n)???
and all your video are just unreal. u made life easy for us.
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why would you add the last step at 22:15? 1/(n+2) is just 1/infinity which is zero. Absolutely no need to multiply top and bottom to get the zero in the numerator
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I'm lost at 19:08. Apparently the answer is now 1, but why couldn't it be 0? sin(1/n) would return 0 and anything multiplied by 0 is 0. Why is that invalid? Are we only able to find the sequence when n only appears once in the function?
Never mind i understand now. The sin of 1/n may approach zero but it never reaches zero. Then it is multiplied by what ever n is as it approaches infinity.
Wait so at 22:55 why do you multiply by 1/n instead of just evaluating the limit there??
last one was amazing
Watching while the online exam
At 13:49, why can you determine it's convergent since lim is 0 here? The divergence test on our slide said that you can't determine whether it's convergent or divergent straight forward if lim=0. I'm so confused:(((
I think you're getting confused between the convergence and divergence of series and of sequences, the divergence test of series needs the limit you're talking about, and in this example we can't determine whether the infinite sum is convergent or divergent(the series) but what we can determine in this example is that the sequence will end up at 0 when we approach infinity
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Well done hussy!
Will give u a good idea about convergence nd divergence.
But formaly the idea of Convergence nd divergence is different.
really helpful, thanks again
for the question at 13:44 couldn't you just simplify sin(n)/n to 1? Is that an identity that can be used?
you are a great help thanks
for 13:21 why can’t we use lopital rule and make it lim cos(n) = 1?
Great video bro thanks it all clea
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