Power+Series

Chris Dulmaine & Clarence Johnson, III Class Date: November 20, 2012 = Power Series: =
 * Definition: A //power series//, based at **x = a**, is a series in the form: [[image:eq1.jpg]]
 * Observation: If we fix a value of x, the above power series becomes a (normal) series which we can test for convergence.

**Example:**




= Radius of Convergence: =

Definition: We say

has a radius of convergence of R if it converges for all |x-a| < R

The Case for Interval of Convergence has 4 possible forms

Use ratio test:
 * -> Finding radius and interval of convergence for a general series**
 * RADIUS:**

Test each end point individually. The ratio test won't help in this case.
 * INTERVAL:**