Is the series $\sum_(n=0)^\infty1/((2n+1)!)$ absolutely convergent, conditionally convergent or divergent?

Question

use the appropriate test...
I know Root wouldn't work with a factorial, but I got stuck on Ratio, too.

I am at $\stackrel(L)(\infty)|1/(2n+2)|$ , what should I put next?

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Answer 1 · 2018-04-23T20:31:26

$"Compare it with "sum_{n=0}^oo 1/(n!) = exp(1) = e = 2.7182818...$

$"Each term is equal to or smaller than the"$

$sum_{n=0}^oo 1/(n!) = exp(1) = e = 2.7182818...$

$"All terms are positive so the sum S of the series is between"$

$0 < S < e = 2.7182818....$

$"So the series is absolutely convergent."$