You want to see if .
For your series you have...
as
(n^sqrt(2) ) / 2^n
I want to determine if this series will converge or diverge. When I use the root test I get sqrt(2)/2 which is less than 1 so it will converge. The book used the ratio test. Could someone please show me how they used the ratio test to say it converges. I got lim n->infinity n/2 which is infinity so it would diverge.