calculus..absolute convergence?

Question

Determine whether the series is absolutely convergent:

1) summation notation symbol (with n=1 on bottom and infinity on top) of n^2/2^n

2) summation notation symbol (with n=1 on bottom and infinity on top) of 10^n/(n+1)4^(2n+1)

Answer 1

Hey, Doc, you still plugging away?

1) Use the Ratio Test to show this series diverges. The ratio of the (n+1)-st to the n-th term is (n + 1)/2, which is not less than 1 as n -> inf.

2) Again, the Ratio Test. This time the ratio is
10*(n+1)/[(4^2)*(n+2)] and the limit as n -> inf is 10/16. And of course the convergence is absolute, because all terms are positive.

Good luck.