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.
Overview
Syllabus
What is a series?.
Geometric Series.
Sum of n/2^n.
A diagonally telescoping sum.
Divergence Test Proof.
Comparison Test Proof.
Limit Comparison Test Proof.
Root Test Proof.
DON'T use Root Test.
Ratio Test Proof.
Ratio vs Root Test.
e is irrational.
The Block Test.
Crazy Sum.
Monster Sum.
Block Test Proof.
COOL Euler.
Integral Test.
Integral Test.
Sum of 1/n^2.
The Euler Mascheroni Constant.
Alternating Series Test Proof.
Convergent squares.
Rearrange a series.
Riemann Series Theorem.
Taught by
Dr Peyam
