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Solved: Interval and radius of convergence Determine the
Chapter 8, Problem 10E(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.
\(\sum(-1)^{k} \frac{x^{k}}{5^{k}}\)
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.
\(\sum(-1)^{k} \frac{x^{k}}{5^{k}}\)
ANSWER:Solution 10EStep 1:Given series is and To determine the radius of convergence we use ratio test which states: The ratio test states that:a. If then the series convergesb. If then the series divergesc. If or the limit does not exist then the test is inconclusive.Calculating L, we get Series converge, if . Using this we writeSo, the radius of convergence for this power series is R=5.