Series Ratio/Root Test, Interval of Convergence, Moments and Center of Mass | Math VOD 2024-05-16 

The VOD of my livestream on May 16, 2024.
Discord: / discord
Twitch: / dondoesmath
Gaming Channel: @DonDoesMathAndGaming
00:00 Drawing Stuff
15:17 Heptagon Problem
01:14:30 Olympiad Triangle Problem
02:06:19 Function Existence
02:19:50 Positive Derivative Implies Increasing Neighborhood
02:43:30 Various Analysis Questions
02:46:50 Series (-1)^n ln(n)/n
02:48:00 Series (-9)^n/(n10^(n+1))
03:04:08 Series (n/ln(n))^n
03:14:28 Series (-1)^n arctan(n)/n^2
03:29:30 Explanation of Series Comparison Test
03:51:00 What is summation?
03:56:02 Interval of Convergence x^n/n
04:09:18 Interval of Convergence sqrt(n)x^n
04:22:43 Interval of Convergence n/(2^n (n^2+1)) x^n
04:38:54 Interval of Convergence (x-2)^n/(n^2+1)
04:46:40 Circle with Squares Inside Question
05:22:06 Moments about x/y-axes, center of mass