Infinite

Σ ln(n/(n+1))

n=1

I know that you have to test and make sure that "a sub n" goes to 0 as n goes to infinite. You could split the summation into Σln(n) - Σln(n+1) and then take the limits as n approaches infinite of each "a sub n" separately, right? You get infinite minus infinite, though. But isn't it possible that these two limits diverge but the sum of them converges?

Thank you