Interval and radius of convergence Determine

Chapter 8, Problem 18E

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QUESTION:

Interval and radius of convergence Determine the radius of convergence of the following power series. Then test the endpoints to determine the interval of convergence.

\(\sum \frac{(-2)^{k}(x+3)^{k}}{3^{k+1}}\)

Questions & Answers

QUESTION:

Interval and radius of convergence Determine the radius of convergence of the following power series. Then test the endpoints to determine the interval of convergence.

\(\sum \frac{(-2)^{k}(x+3)^{k}}{3^{k+1}}\)

ANSWER:

Solution 18EStep 1:In this problem we have to determine the radius of convergence of the power series.Use Ratio test to determine the radius of convergence.If there exists an N so that for all , and and1. If L<1, converges.2. If L>1, diverges.3. If L=1, the test is inconclusive.

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