Sum of Sequence of Products of Consecutive Reciprocals/Proof 2

Proof
We can observe that:
 * $\displaystyle \frac 1 {j \left({j + 1}\right)} = \frac 1 j - \frac 1 {j + 1}$

and that $\displaystyle \sum_{j \mathop = 1}^n \left({\frac 1 j - \frac 1 {j + 1}}\right)$ is a telescoping series.

Therefore: