Solution Found!
Interval and radius of convergence Determine
Chapter 8, Problem 18E(choose chapter or problem)
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.