Explore key concepts in calculus through a comprehensive 90-minute video lecture focusing on series, including geometric, telescoping, and harmonic types. Dive into convergence of sequences versus series, examine multiple examples of geometric series, and understand the harmonic series. Learn about the test for divergence and tackle challenging problems involving partial sums, trigonometric functions, and complex textbook exercises. Master techniques for solving telescoping series with arctangent functions and gain insights into tricky calculus problems that require careful analysis.
Calculus - Series - Geometric, Telescoping & Harmonic
Overview
Syllabus
Series, 11 2 #15, Conv of Seq vs Conv of Series.
Series, 11 2 #19, Geometric Series.
Series, 11 2 #21, Geometric Series (with extra example).
Series, 11 2 #23, Geometric Series.
Series, 11 2 #27, Harmonic Series.
Series, 11 2 #31, Geometric Series.
Series, 11 2 #33, Sigma nth root of 2.
Series, 11 2 #35, Test for Divergence.
THE FACT.
telescoping series of arctan(n)-arctan(n+1).
Series, 11 2 #50.
Q215, given partial sun, find an.
Series (1+1/n)^n, test for divergence.
series of cos(1/n), test for divergence.
telescoping series of arctan(n)-arctan(n+1).
a HARD calc 2 textbook problem (don't get tricked!).
Taught by
blackpenredpen
Related Courses
-
Calculus - Direct & Limit Comparison Test
-
Calculus 2 - Series, Geometric Series, Harmonic Series, and Divergence Test
-
Introduction to Advanced Calculus
-
A-level Mathematics for Year 13 - Course 1: Functions, Sequences and Series, and Numerical Methods
-
Calculus - Strategies for Testing Series
-
Calculus - Ratio & Root Test
