i need help on this question. i cant get the ans finally.(i did the working outside) where's my mistake and how should i proceed?
I didn't look at this in great detail, but what is r? It shows up in your summation but not in the expression being summed up. If I had to guess I'd say that one of your sums should be:
$\displaystyle \sum_{r = 1}^n \frac{1}{r + 2} \neq \frac{1}{n + 2}$