How do you use the ratio test to test the convergence of the series $\sum \frac{8^{n}}{n!}$ $∑ (8^n)/(n!)$ from n=1 to infinity?

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Answer 1 · 2015-10-15T16:48:26

The series would converge.

To test the convergence apply the ratio test which means to find

$lim_ (n->oo) (a_(n+1) /a_n)$ . If limit is <1, the series would converge. In the present case this limit is,

= $lim_ (n->oo) (8^(n+1))/((n+1)!) * (n!)/8^n$

= $lim_ (n->oo) 8/(n+1)$ =0.Hence the series would converge.

How do you use the ratio test to test the convergence of the series ∑ (8^n)/(n!)∑8nn!∑ (8^n)/(n!) from n=1 to infinity?