Find the sum of the first ten terms How do I find the sum below?
$$\sum_{i=1}^{10}\frac{2i+1}{i^2(i+1)^2}$$
I think there should be a simpler way instead of just adding the ten terms up using brute force, since it's impossible to do that in less than 10 minutes in a contest, because the terms starting on the 4th one is ugly, and even uglier to get the common denominator.
Can someone give me some idea for this?

Note that
$$
\frac{2i+1}{i^{2} (i+1)^{2}}
=
\frac{1}{i^{2}} - \frac{1}{(i+1)^{2}}.
$$
See under telescoping series.
