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1
What is a series?
2
Geometric Series
3
Sum of n/2^n
4
A diagonally telescoping sum
5
Divergence Test Proof
6
Comparison Test Proof
7
Limit Comparison Test Proof
8
Root Test Proof
9
DON'T use Root Test
10
Ratio Test Proof
11
Ratio vs Root Test
12
e is irrational
13
The Block Test
14
Crazy Sum
15
Monster Sum
16
Block Test Proof
17
COOL Euler
18
Integral Test
19
Integral Test
20
Sum of 1/n^2
21
The Euler Mascheroni Constant
22
Alternating Series Test Proof
23
Convergent squares
24
Rearrange a series
25
Riemann Series Theorem
Description:
Dive into a comprehensive exploration of mathematical series through this 5-hour educational content. Learn the fundamentals of series, including geometric series and the sum of n/2^n. Explore advanced topics such as divergence and comparison test proofs, limit comparison test, and root test. Discover why the root test should be avoided in certain scenarios and compare it with the ratio test. Investigate the irrationality of e, the block test, and its proof. Tackle challenging sums, including the "Crazy Sum" and "Monster Sum". Delve into the Euler-Mascheroni constant, the integral test, and its applications. Examine the alternating series test proof, convergent squares, and the rearrangement of series. Conclude with an in-depth look at the Riemann Series Theorem, providing a solid foundation in series mathematics.

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