Question

Will award medal
how does the series Σ N=1 -> infinity (2^n/n!) converge.

Answer 1

Ive used the ratio test and got 2/(n+1)

Answer 2

@sidsiddhartha is 2/(n+1)=0 as limn->infinity, because you have a numerator on the top but since the denom is getting so big it is actually making it zero. so it converges?

Answer 3

i think ratio test wont work here u can try raabe's test. i'll come back in an hour then i'll to solve it :)

Answer 4

yeah \[\lim_{n \rightarrow \infty}2/n+1\rightarrow 0 <1\]
so by alemberts ratio test if limit<1 then it is convergent
@pmkat14

Answer 5

so with any constant in the numerator, and any n, or n! in the denominator, as n-> infinity, the series goes to zero?