1. 9.8 Interval of convergence

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

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

4. 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→ negative harmonic series
Converges Diverges
(also a p series with p=1)
Interval is -1<x<1
Note: the radius of converges is 1

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

6. 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/ Interval of convergence is (-7,7)

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

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

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

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

11. Homework p odd