Chapter 11 - Section 11.6 - Absolute Convergence and the Ratio and Root Tests - 11.6 Exercises: 11

$\Sigma\frac{1}{k!}$ $\lim\limits_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\frac{1}{(k+1)!}\times\frac{k!}{1}|=\lim\limits_{n \to \infty}|\frac{1}{k+1}|=\frac{1}{\infty}=0$. Convergent.

Work Step by Step

Using the ratio test we find that the limit equals 0. Since 0<1 it can be stated that the series is absolutely convergent.

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