Intro to Infinite Series | Real Analysis

We introduce the definition of infinite series, the definition of a convergent series and the limit of a series, as well as divergent series. We'll discuss partial sums, terms of an infinite series, and look at various examples including geometric series, the harmonic series, and p-series. We'll also discuss Zeno's Paradox about an arrow headed for a target, which seemingly cannot get there! #RealAnalysis

Table of Contents
0:00 Into
1:57 Zeno's Paradox
7:42 Definitions
14:12 Examples

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[strncatt]

I'm 100% sure that I would have given up self studying analysis without this real analysis series! best videos on the topic hands down

[strangergerman]

Thanks for making this video it helps me a lot!

[tomkerruish]

16:21 Or maybe -1/12. (Who am I to argue with Ramanujan?) Just like the product of all positive integers is sqrt(2 pi).
Edit: oh, you're starting with k=0, not k=1? For maximal confusion, that really can make a difference.
Second edit: going from the Wikipedia article on 1+2+3+4+..., changing f(x)=x to f(x)=x-1 should add +½ to the sum, resulting in the new sum 0+1+2+3+... = +5/12.

[satish]

7:50 is infinite series a sum? like infinite series is just one number(sum of ak's)? aren't series(in general) seperated by comma? like 1, 1/2, 1/3, 1/4, instead of which would just give one single number). How is the latter one a series if it is giving us the sum?

[suyogyadahal-me]

If we are assuming half of distance to be 1/2 (whole distance divided by 2) does not that mean that full distance is 1 What an irony of mathematics. if we assume whole distance to be 2 units than half distance would be 2/2 :D .