Series

This course is a part of Integral Calculus, a 5-course Topic series from Khan Academy.

Series are sums of multiple terms. Infinite series are sums of an infinite number of terms. Don't all infinite series grow to infinity? It turns out the answer is no. Some infinite series converge to a finite value. Learn how this is possible and how we can tell whether a series converges and to what value. We will also learn about Taylor and Maclaurin series, which are series that act as functions and converge to common functions like sin(x) or eˣ.

This course contains 18 segments:

Convergent and divergent infinite series

Infinite geometric series

nth-term test

Integral test

Harmonic series and p-series

Comparison tests

Alternating series test

Ratio test

Absolute and conditional convergence

Alternating series error bound

Taylor and Maclaurin polynomials intro

Lagrange error bound

Power series intro

Function as a geometric series

Maclaurin series of eˣ, sin(x), and cos(x)

Representing functions as power series

Telescoping series

Proof videos