# Real Analysis : Radius and Interval of Convergence - Power Series (3 Problems)

Determine the radius of convergence and the exact interval of convergence of the following power series...

Please see attached.

Â© BrainMass Inc. brainmass.com March 4, 2021, 6:08 pm ad1c9bdddfhttps://brainmass.com/math/real-analysis/real-analysis-radius-interval-convergence-power-series-31014

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

Solution.

(a) For

We know that if a power series converges, then it converges absolutely. So, we consider . We have the ratio of the n+1 term and the n-th term is

If , then converges. So,

converges. So, we know that the radius of the convergence is .

Now we consider ...

#### Solution Summary

The Radius and Interval of Convergence of Power Series are found. The solution is detailed and well presented. The response received a rating of "5" from the student who posted the question.

$2.19