Power Series

AP Calculus · Axiom Academy

Functions defined as infinite polynomials A power series centered at a is . It converges on some interval centered at a (possibly just the single point a , or all of ). Finding the Radius of Convergence Use the Ratio Test : (or Root Test). : ratio unless x = 0 . So R = 0 . Every power series has a radius of convergence Converges absolutely for |x - a| R Must check endpoints separately

This is the written version of the interactive lesson above. See the full AP Calculus course.