Evaluating Partial Sums I need some help with the following question from my homework, I do not exactly understand what to do. Question at Hand
Text is: Evaluate the partial sums of the infinite series $\displaystyle \sum_{n=1}^\infty \frac1{n(n+2)}$, and then evaluate the infinite series. 
The trouble I am having is understanding exactly what is asked of me to do.

The m-th partial sum of $ \displaystyle \sum_{n=1}^{\infty} \frac{1}{n(n+2) } $ is the sum truncated to the m-th term. In other words, it first wants you to find the finite sum $$ s_m = \sum_{n=1}^m \frac{1}{n(n+2)} $$ for all $m\in \mathbb{N}$. Then it wants you to find the original infinite sum by recalling the definition that $$  \sum_{n=1}^{\infty} \frac{1}{n(n+2) } = \lim_{m\to \infty} s_m .$$
