Question

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

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?

Answer 1

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

Explanation:

`"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."`