Question
Asked Jul 26, 2019
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Determine 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
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Determine 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

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Expert Answer

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.

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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:

<18
<1
18
O1
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<18 <1 18 O1

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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...

A18
18x 18
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A18 18x 18

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Calculus

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