Help with showing infinite series converges/diverges

[coreluccio]

Homework Statement

Determine whether the series converges or diverges

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

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.

 

[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?