Problem 16RE

Radius and interval of convergence Use the Ratio or Root Test to determine the radius of convergence of the following power series. Test the endpoints to determine the interval of convergence, when appropriate.

Solution 16RE

Step 1:

Given series is and

To determine the radius of convergence we use ratio test which states:

The ratio test states that:

a. If then the series converges

b. If then the series diverges

c. If or the limit does not exist then the test is inconclusive.

Calculating L, we get

Series converge, if . Using this we write

So, the radius of convergence for this power series is R=1.