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Radius and interval of convergence Use the

Chapter 1, Problem 20RE

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QUESTION:

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.

\(\sum \frac{(x+2)^{k}}{\sqrt{k}}\)

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QUESTION:

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.

\(\sum \frac{(x+2)^{k}}{\sqrt{k}}\)

ANSWER:

Solution 20RE

Step 1:

 Here we have to determine  the radius of convergence of the .

                 is  a power series .

               If the power series  converges for |x − c| < R and diverges for |x − c| > R, then 0 ≤ R ≤ ∞ is called the radius of convergence of the power series.

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