S01.5 Infinite Series

MIT RES.6-012 Introduction to Probability, Spring 2018
Instructor: John Tsitsiklis

License: Creative Commons BY-NC-SA

[JinxedG]

Started doing this lecture because I missed doing math and had a side project I wanted to start working on for fun (programming something with probability as a key focus, user inputting different numbers for variables), but wasn't confident I was using the right formulas for the given situations, so here I am! And now I'm realizing that I should probably go and find a basic calculus course to refresh myself as the majority of the S01 are not taking. But I love learning all this and wish all these sources were available back when I was in school (and also that I didn't major in Communications, but oh well. Decade plus ago). If only I could go back to school at my age, but here's the next best thing really

[SecretEscapist]

Thanks a lot for this amazing lecture

[christaylor]

This video does not rigorously define what a number series is. More formally, a number series is a pair (q, sums(q)) of number sequences, where sums(q) is the sequence of partial sums of the sequence q. In standard notation, the expression Sigma q is used to denote both the series itself, and the sum-value of the series, which if q is infinite and sums(q) converges, equals the limit of sums(q). Thus Sigma q =1 means that the series Sigma 1 converges and has the sum-value 1.

[BELLAROSE]

Does exist …. And with both limits….
Values are then transcendental, whereby both irrational and rational existence occurs showcasing both limits suggest very hard to compute by computer alone, does require mathematics by humans ….

[yuhangtao]

1:34 I think if the monotonic sequences converge to an infinite, then the limit won't exist.