Hello everyone,

I have checked some post about sum here but...

There is this Serie:

(2n+1)/n^2(n+1)^2

with n=1 to infinity

Actually this is an easy one,

I do partial fraction decomposition and come up with 1 - 1/(n+1)^2 and the limit of the last is the sum of the Serie (I am now learning series).

However I have a question,

why I cannot go directly take the limit from the very begining, which results to zero and say that the sum is zero.
I know this is not right, but I cannot really express it why, taking the sum even for n=2 it immediately shows that my guess is wrong. Is there something more to give as an answear to my question?

Thank you all guys

,

and I am sorry if it is not a very clear question!