This course covers the concept of series, including geometric series, diagonally telescoping sums, and various convergence tests such as the divergence test, comparison test, limit comparison test, and more. Students will learn about the Euler Mascheroni constant, alternating series, and how to rearrange a series. The teaching method includes proofs, examples, and applications. This course is intended for learners interested in advanced mathematics and calculus.
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
