Calculus 2 Lecture 9.1: Convergence and Divergence of Sequences

[@xPa7r1cKx]

0:00 introduction into sequences 4:35 examples 17:55 patterns 36:56 recursive sequences 43:42 limits of sequences 50:10 convergence or divergence? 1:07:15 squeeze theorem 1:37:50 monotonic sequences 2:00:08 bounded sequences For the lazy :)

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[@ProfessorLeonard]

Samuel McCandless Please note that this lecture is dealing with SEQUENCES not SERIES. The convergence test for Sequences is very basic and is correctly stated in the lesson. The Divergence test that you reference is absolutely correct, but only for Series. Please visit the remaining lessons in the "Chapter" to see what I mean. Cheers and thanks for watching!! Professor Leonard

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Professor Leonard at 59:00 you mention the "old school" of indeterminate form of a limit instead of L'Hospital's rule. This involves dividing all the terms with the highest degree n in the denominator. If that same n has a coefficient, does that also get included when dividing the the terms?

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[@ProfessorLeonard]

I'm so glad to hear of your success considering your struggles!

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[@Stefabro]

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im glad this helped you but this class it not a typical college math class. professor leonard babies us in these lectures. college math is different. you only have 50 mins, not 2 hours. the best advice: READ AND TRY TO DO THE LESSON BEFORE CLASS so you will at least have a basis of understanding!!!!!!

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professor leonard, thank you so much for these videos. i am a bio major who made the mistake of taking calc 2. i got a D on the first exam, started watched your lectures, and got a B on the second. i'm still doing bad, but i feel like everything will be okay with the motivation you give me (: i usually don't comment like this but i am so thankful to you

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[@Mohammed-qr6gq]

Limit of a sequence (convergence and divergence) starts at: 43:45

[@lollolzi2996]

Why does he write '' less than '' as less than or equals to? For an example, if you want to say that the number n is smaller than M, instead of writing n < M he writes n _M instead of n>M These are some examples 2:00:28 to 2:00: 48

[@jameswhyte1340]

This clicked immediately with me. Thanks you for being so patient in your teaching. Can't wait to watch all you videos on sequences and series!

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Thanks professor! Due to the coronavirus my calc2 class has gone virtual. I am pretty old school and really do better in a classroom setting. You do such a great job at taking the time to make sure everyone understands the concepts, and your explanations are understandable. Definitely will be subscribing!

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[@captaingerbil1234]

I'm taking Calculus 2 during Covid times, so I'm taking it online. I'm pretty sure the retirement age professor that I have has never taught an online class before. The notes are completely illegible, he has a heavy Ukranian accent, and he doesn't explain things, he only shows you them and asks "Do you see?" When you respond, "No, I do not see." He says says, "Look right here. See? Do you see? Ok. So, moving on." I don't even watching the lectures and I only go through the notes to try to pick out the main objectives to learn for the test. Brofessor Leonard, you're a math hero. Your lectures and the Openstax text books have taught me 80% of the calculus that I've learned. Thank you.

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if only all my professors in college were like you, I'd ace every class. kinda sucks that you don't teach the rest of the chapters but I'm sure as hell thankful that you at least covered all of chapter 9. 👏

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Professor. This is after 6 years am enjoying a lesson this much and didn't bother to look up to the clock. Keep up the good work!

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Linear Algebra and Number Theory lectures please.

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How did you do?

[@TheTalmon18]

***** Got a 96, could've been 100 lol. But I got 100 on my final. Just finished the next class last week, calc 3. Was pretty tough :[ Think I got an A though. Maybe.

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Monotonic sequences (increasing and decreasing sequences) starts at: 1:37:49

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half a thousand people don't know calculus

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[@TheLychie]

1:37:38 --> "Is that interesting or what?!" "what"

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34:54 almost made me spit out my drink!

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You seriously are a Godsend! I'm taking an online Cal 2 course, I have horrible anxiety and hate asking questions to the professor. I've been trying my best to learn all this on my own and it hasn't been easy. I get stuck a lot and it's frustrating. I was even on the verge of just giving up! But you make it look so easy!! Plus I listened to your introductory lesson about studying and I really need to take that advice. I took Cal 1 in a one month long course...during the final, I would get stuck half way on each problem and totally bombed it. Still passed though, but what you said made so much sense about not fully interalizing it all. Obviously I retained SOME info, just not all. (Yet I think it's totally understandable for a short class.) Hoping to take your advice and do better this time around in Cal 2! Thank you!!!

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Wow what a fantastic series of lectures! I haven't done maths since high school, nearly 40 years ago so hadn't come across a lot of this stuff, but I understood all of it. Very good, clear teaching. Thanks

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59:56 - "yes", I'm almost certain it's impossible to sound more disinterested and still answer a question

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I actually kinda like that girl's voice, she sounds cute.

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you gay?

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arent we all?

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professor, will you be uploading calc 3 lectures?

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He plans to make calculus 3 videos in the spring semester.

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he already does

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I like the way you explain the topic like it’s new and not cannon. So that anyone can just start as doesn’t have to watch all 13 previous video to understand what you’re saying

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[@douggwyn9656]

Just because a monotonically increasing sequence has an upper bound M does not mean that its limit is M. It only means that it has *some* limit which cannot be greater than M; it may be less than M. Now, if M were the *least* upper bound, the limit would be exactly M. Similarly for monotonically decreasing and greatest lower bound.

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Professor Leonard sir i understood everything and you just made it lot more easier since i was not understanding in my class .i am from china .A big thanks to you.