Hello all:

I seen this summation problem and was wondering what insight the learned on this site have:

Given $\displaystyle \frac{2-r}{r(r+1)(r+2)}=\frac{2}{r+2}-\frac{3}{r+1}+\frac{1}{r}$, show that $\displaystyle \sum_{r=1}^{n}\frac{2-r}{r(r+1)(r+2)}=\frac{2}{n+2}-\frac{1}{n+1}$

I ran this through Maple and got $\displaystyle \frac{2}{n+2}-\frac{1}{n+1}$

but how is that derived?. I tried partial sums but hit a wall. It may be easier than I am making it.