Calculus 2 Lecture 9.4: The Comparison Test for Series and The Limit Comparison Test

Calculus 2 Lecture 9.4: The Comparison Test for Series and The Limit Comparison Test

[jasontaylor]

Tell me: "Does that make sense to you?"

I LOVE this method of teaching. Thank you.

[teachingkidsyoga]

IDK where you learned to teach, but you make Calc 2 seem so easy now, i had a hard time understanding until I watched your videos. Thank you.

[michaelscepka]

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[CattyMcDaddy]

Best mathematics teacher on the planet. "show of hands if you understand this" always slowing down if his students don't get something, which is RARE because the way he teaches is flawless. If I had you as my calc teacher for 1 through 3, I would be a mathematician.Thank you for being amazing

[MileeWilson]

Probably the best and most sane Math teacher I know.

[yagmurbugucoskun]

48:57 He summarises what to do step by step from Lecture 9.1 to 9.4

[lllWiseManlll]

Professor Leonard : That's the IDEA
Me : level of understanding = 99.99%
Professor Leonard: *goes over the example one more time really quick*
Does that make sense to you?
Me: level of understanding = 100%

THANK YOU SO MUCH GTL . Great Teach Leonard!!

[dulcedelgado]

Thank you so much for these videos Professor Leonard! Now in 2020 they are still helping students all around the world during this pandemic crisis. God bless you.

[mmartinez]

I usually watch PatrickJMT's shorter videos for calc review, but taking the time to watch your videos has made me more at ease than anything else I've come across for understanding concepts that once seemed so abstract. Thanks Professor!!

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9 years later, and still the best Mathematics Professor I could find on the damn website, idk people in high school told me that no one in a college would ever explain things to you with example, well, guess I found the diamond

[jimmidge]

I.m 83 and remember failing Calc back in 1951 ..Wish you were there. One knock Ya jus gotta write largerjimmidge

[jonnymat]

Here's a little trick I use to remember when a Direct Comparison Test shows convergence or divergence:

Just remember:
1.) "  a Smaller Cat"
* When a(sub n) is Smaller & b(sub n) Converges: Converges
2.) "a Bigger  Dog” 
* When a(sub n) is Bigger (or larger) & b(sub n) Diverges: Diverges

Hope this helped! I used cat and dog because it was easy for me to remember but feel free to use your imagination 

[amadif]

I can't believe I only started using this guy's videos 2 days before my calc final. The style and pace of teaching is excellent. Thankfully he has a calc 3 playlist, which I will be using a lot!

[foeva]

This is literally the first time, after repeating the course 3 times, that i have understood direct comparison test. Thank you so much professor Leonard

[lycybin]

frick this guy has helped me so much. Wish I could send a letter or something just thanking him. I was struggling so much in calc 2 since it is so much more dense and you need to remember pretty much EVERYTHING from calc 1 and ALL other prerequisites in their most advanced forms and prof Leonard just goes through it so smoothly and breaks it down so well. On my first calc 2 test I received a 48, and then started watching him after that and on my second test I got an 85! Plus his sense of humor makes it even easier to watch and follow along with his lectures and not get bored. Prof. Leonard if you see this, I am so thankful for you,

[meksudbuser]

Professor Leonard, you are creating future scientists. You are very organized, clear, and logical. The best mathematics professor I have ever seen in my educational journey.

[funnypython]

Professor Leonard, the least thing i can say that you are a LEGEND, THANK YOU SO MUCH PROFESSOR LEONARD FOR THIS AMAZING GREAT TEACHING OF CALCULUS 1, 2, 3...., i have been with since precalc and here i am going to differential equations and i want to tell u that i scored the highest grade is all of these calculus courses and this is for a single reason, You are the teacher, thank you Professor

[dantesinaguglia]

Such a great Professor, I go to university in Ontario, Canada, (Zoom currently) I don't even attend my calc 2 lectures anymore, he teaches so well! Ive recommended so many classmates.

[freekeyboards]

He does an amazing job at 57:30 of tying all this together based on a student's question. He really weaves the concept of sequences, series, limits, converging, and diverging really well. That part alone is worth its weight in gold.

[neokattan]

I like his method of teaching so much because if I'm in the middle of a test and i forget if if something is a + or a - or if something is square root or squared, I know where it all started so I can figure it out. Instead most teachers make you memorize 6 equations when you could be learning this way and only memorizing the 1 that they were derived from and being able to derive them yourself.