# Math Help - Convergence of Series

1. ## Convergence of Series

Please help me with this!!!

Determine if the following series converge or diverge.

a) the sum from n=1 to infinity of [n/3n+1]^2n

b) the sum from n=2 to infinity of [1/(n(ln)^1/2)]

I don't know what test to use with this series (comparison, ratio, integral etc)?

thank you for your help

2. Hi

Originally Posted by kithy
Please help me with this!!!

Determine if the following series converge or diverge.

a) the sum from n=1 to infinity of [n/3n+1]^2n
I don't know what test to use with this series (comparison, ratio, integral etc)?
The comparison test works : $0\leq \frac{n}{3n+1}=\frac{1}{3+\frac{1}{n}}\leq \frac{1}{3}$

b) the sum from n=2 to infinity of [1/(n(ln)^1/2)]

I don't know what test to use with this series (comparison, ratio, integral etc)?
You can use integrals : $\int \frac{1}{t \sqrt{\ln t}} \,\mathrm{d}t=2\int \frac{u'(t)}{2\sqrt{u(t)}} \, \mathrm{d}t$ with $u(t)=\ln t$ can be quite easily evaluated.