# Convergence of series using ratio test

1. Sep 24, 2011

### l888l888l888

1. The problem statement, all variables and given/known data
assume summation of series An converges with all An>0. Prove summation of sqrt(An)/n converges

2. Relevant equations

3. The attempt at a solution
I Tried using the ratio test which says if lim as n goes to infinity of |Bn+1/Bn|<1 then summation of Bn converges. I let Bn be Sqrt(An)/n and we have...

lim as n goes to infinity of |(sqrt(An+1/An)*n/n+1|. limit of n/n+1 goes to one so i need to prove that |sqrt(An+1/An)|<1. But I got stuck because just because An converges does not mean that |(An+1/An)|<1. Can someone help me or suggest on a different convergence test that I should use?

2. Sep 24, 2011

### Staff: Mentor

$$\lim_{n \to \infty} \sqrt{\frac{a_{n+1}}{a_n}} = 1$$