Are you sure you wrote this correctly? $\displaystyle (2-1) = 1$ so$\displaystyle ...$
$\displaystyle \frac{1}{n-1}+\frac{1}{n(n-1)} = \frac{n}{n(n-1)}+\frac{1}{n(n-1)} = \frac{n+1}{n(n-1)}$