To find , we may begin with the fact that
How can this sum be simplified?
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?