Math Help - partial fractions for summing series

1. partial fractions for summing series

how did it find this 1-1/(n+1) ?

if is subtract 1/n - 1/n+1 the result is different

2. Re: partial fractions for summing series

Basically saying all the terms $\frac{1}{2}, \frac{1}{3}, ..., \frac{1}{n}$ terms get cancelled out leaving you with a 1 from backet 1, and $\frac{-1}{n+1}$ from bracket 2, so you get $1 - \frac{1}{n+1}$