# Help with showing infinite series converges/diverges

1. Feb 26, 2012

### coreluccio

1. The problem statement, all variables and given/known data

Determine whether the series converges or diverges

1/2(ln(n+1))^2 from n = 1 to infinity

3. The attempt at a solution

Cannot find anything to compare this series to that will show it diverges. Ratio and root test both fail. Integral test requires integrating to a non-elementary anti derivative. I have no clue how to find a solution to this.

2. Feb 26, 2012

### Dick

You probably mean $\frac{1}{2 \ln(n+1)^2}$, think about comparing it with $\frac{1}{n}$. Which do you think is larger for large values of n? Now can you prove it?