is divergent.

I understand what the solution is saying (multiplying and eliminating everything except end terms....), but I couldn't figure out what I did wrong using the integral test: f(x) = ln (1+1/x) is decreasing, and positive, so . Then letting y = x + 1 yields . It is integrating the same function from different starting points, won't the difference be a finite area?

Can anyone explain? Thanks!