- #1

mikky05v

- 53

- 0

## Homework Statement

I have been working on this proof for a few hours and I can not make it work out.

$$\sum_{i=1}^{n}\frac{1}{i(i+1)}=1-\frac{1}{(n+1)}$$

i need to get to

$$1-\frac{1}{k+2}$$

I get as far as

$$1-\frac{1}{k+1}+\frac{1}{(k+1)(k+2)}$$

then I have tried

$$1-\frac{(k+2)+1}{(k+1)(k+2)}$$

by multiplying the left fraction by (k+2) which got me nowhere.

What am I doing wrong?