Hi guys, quick Question

For the series $\displaystyle \sum_{i=1}^\infty(\frac{1}{k}-\frac{1}{k+2})$ find a formula for $\displaystyle S_n$

I know that every number will cancel out but $\displaystyle 1 $ and $\displaystyle \frac{1}{2}$ but the answer is $\displaystyle 1+\frac{1}{2}-\frac{1}{n+1}-\frac{1}{n+2}$.

How do we get $\displaystyle -\frac{1}{n+1}-\frac{1}{n+2}$?

Thx!