# Determine the radius of convergence of the following power series. Then test the endpoints to determine the interval of convergence.kX18The radius of convergence is R

Question
19 views help_outlineImage TranscriptioncloseDetermine the radius of convergence of the following power series. Then test the endpoints to determine the interval of convergence. k X 18 The radius of convergence is R fullscreen
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Step 1

We have been given a power series and we are required to find its radius of convergence as well as interval of convergence.

Step 2

We know that the given power series is a geometric series, and a geometric series is convergent when its common ratio is between -1 and 1. Therefore, we can set the condition for convergence of the given power series as:

Step 3

Thus, the radius of convergence of the given power series is 18.

We can now find the interval of convergence by solving this inequ...

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### Calculus 