Determine whether each is convergent or divergent. Is either absolutely convergent? The sum of...

Question:

Determine whether each is convergent or divergent. Is either absolutely convergent?

{eq}\sum\limits_{n = 0}^{\infty} \frac{(e^n)}{(n!)}. {/eq}

Answer and Explanation:

{eq}L = \mathop {\lim }\limits_{n \to \infty } \left| {\frac{{{e^{n + 1}n!}}}{{{e^n(n+1)!}}}} \right|\\ L = \mathop {\lim }\limits_{n \to \infty } \left| {\frac{{{e}}}{{{(n+1)}}}} \right|\\ L=0\\ L <1 {/eq}

This implies given series is absolutely convergent.


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