9.8 Interval of convergence

From the 2011 AP Calc BC exam Find the interval of convergence

From the 2011 AP Calc BC exam Use the ratio test (use with Absolute value) lim xn+1 . n n→∞ n+1 xn Simplifies to x lim n/n+1 = x lim x n n→∞ n→∞ n+1 by the ratio test -1<x<1 What about the end points?

From the 2011 AP Calc BC exam Try x =1 Try x = -1 (-1) n+1 1/n (-1) n+1 (-1)n/n Alternating series = -1/n Nth term→0 negative harmonic series Converges Diverges (also a p series with p=1) Interval is -1<x<1 Note: the radius of converges is 1

Problem 12 Find the Interval of convergence. Check for convergence on the end points

Problem 12 Find the Interval of convergence. Check for convergence on the end points This is a geometric series. It converges when │r │< 1 r = x/7 Interval of convergence is (-7,7)

Find the Interval of convergence Find the Interval of convergence. Check for convergence on the end points

Find the Interval of convergence Find the Interval of convergence. Check for convergence on the end points

Find the Interval of convergence Find the Interval of convergence. Check for convergence on the end points

Find the Interval of convergence Find the Interval of convergence. Check for convergence on the end points

Homework p. 668 5-31 odd