Proof by induction - fractions

[mikky05v]

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?

 

[mikky05v]

disregard, I figured it out. I simply had to separate 1/i(i+1) into 1/i - 1/(i+1)