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Choose your test Use the test of your choice
Chapter 12, Problem 43E(choose chapter or problem)
40-57. Choose your test Use the test of your choice to determine whether the following series converge.
\(\sum_{k=1}^{\infty} \frac{2^{k} k !}{k^{k}}\)
Questions & Answers
QUESTION:
40-57. Choose your test Use the test of your choice to determine whether the following series converge.
\(\sum_{k=1}^{\infty} \frac{2^{k} k !}{k^{k}}\)
ANSWER:Problem 43EChoose your test Use the test of your choice to determine whether the following series converge. SolutionStep 1In this problem we have to determine whether the seriesconverge or not.Let us use ratio test to find the whether the series converge or not.Ratio test:Let be a sequence of nonzero terms and let . Then 1. If L < 1 then is convergent.2. If L > 1 then is divergent. 3. If L = 1 then nothing can be said about the series. In other words, we say that the ratio is inconclusive.