Calculus 2 Lecture 9.2: Series, Geometric Series, Harmonic Series, and Divergence Test

Calculus 2 Lecture 9.2: Introduction to Series, Geometric Series, Harmonic Series, and the Divergence Test

[Fluxtrance]

If you're like me and reviewing for an exam, here are some time stamps!

Steps for solving Infinite Series: 19:20
Geometric Series: 51:20
Harmonic Series: 1:28:03
Divergence Test: 1:51:08

[elihodges]

Shoutout to the classroom for also being confused when I'm confused.

[hazimrassam]

Introduction to Series 0:00
Telescoping Series 27:20
Geometric Series 51:20
Harmonic Series 1:28:05
Divergence Test 1:40:00
Properties of Convergent Series 1:42:11
The rest is just more examples

[Corypro]

Between his clever humor, delivery/ enunciation, and clear concise breaking down of steps. This man deserves an award. At least from youtube or something. My calculus 2 teacher is the COMPLETE OPPOSITE of Prof. Leonard. Gets mad when you ask questions and doesn't explain things clearly and doesn't seem to care about the well-being of us students. As an aspiring math teacher to be, you are a great role-model and I hope I can be half the teacher you are.

[Zercul]

Please live forever. You helped me so much and I can only imagine the good you would do with an extra hundred years or so.

[UnforsakenXII]

Not only are Leonard's videos a godsend but so is the replay button.

[ilchrist]

My college professor is a very nice person but presents material in a very disorganized manner. I've been struggling through Calc 2 by watching youtube videos, reading the book, and visiting Khan Academy and your lectures have been such a huge help. I just wanted to say thank you.

Thank you!

[thebassofmontecristo]

There is nothing so valuable to math understanding like a Socratic, conversational style of teaching. Personally, I don't think I would have ever understood series if it wasn't taught the way it was on this video. The first 17 minutes of this video were eye-opening to me and once I saw WHY the existing (converging) limit of a partial sum HAS to be the actual sum of an infinite series I stood in awe of the paradoxical simplicity and depth of this topic. This is the beauty of numbers at work. Professor Leonard, you just added to my love of mathematics today. Thank you.

[hajarx]

I actually raise my hand every time you say so.. 

[djx]

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[chemistkriegs]

He is probably the best teacher at math I have ever seen. 100X better than my calc 2 professor now. This is definitely my 'go to' for calc 2. Maybe I will get higher than a 40% for my next exam learning from him instead of my professor now...

[malloryakikonoramiller]

I honestly don't get how you make this so easy to understand.

[potatopotato]

He's literally so nice. His lectures are like ASMR, as in his delivery, his humor, his niceness - genuine concern whether his students understand, his super detailed explanations. I laugh when he makes a joke and instinctively raise my hand whenever I get a problem. I love how he goes over basic algebra becaue I'm not too fast, like I can't see the steps in my head.

[Tuffadandem]

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[Max-iipj]

I don't go to lectures, I only watch Professor Leonard

[limphomofoka]

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[GriffinPearson]

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[mitchellb]

Professor Leonard is an awesome supplement to my class. My teacher is pretty good, but I often need to listen to it a second time, so i just put it on 2 times the speed and I understand that material fairly well.

[kodya]

Series and sequences have been the first time studying math where I have broke down from pure frustration. Thank you for taking the time to teach us this the way it should be taught!

[navee]

Difference between you and my current professors: They only teach me how to do something, you help me understand WHY I'm doing something and THEN show me how to do something properly. Your lessons always stick with me, Professor Leonard, other professors' lessons never do! They always go right over my head. Thank you for what you do!