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?

1692 views around the world

You can reuse this answer
Creative Commons License

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."#