Infinite sequences and series

This course is a part of AP®︎ Calculus BC, a 12-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 16 segments:

Defining convergent and divergent infinite series

Working with geometric series

The nth-term test for divergence

Integral test for convergence

Harmonic series and p-series

Comparison tests for convergence

Alternating series test for convergence

Ratio test for convergence

Determining absolute or conditional convergence

Alternating series error bound

Finding Taylor polynomial approximations of functions

Lagrange error bound

Radius and interval of convergence of power series

Finding Taylor or Maclaurin series for a function

Representing functions as power series

Optional videos

Some things are not explicitly required by the AP Calculus BC course, but many teachers cover them and we also find them useful. We've gathered those optional videos here for your convenience.