$\displaystyle \frac{1}{1*2} + \frac{1}{2*3} + \frac{1}{3*4} + ... + \frac{1}{(n(n+1))} = \frac{n}{n+1}$

I have evaluated it for 1:

$\displaystyle \frac{1}{(1(1+1))} = \frac{1}{1+1} = \frac{1}{2}$

same with k:

$\displaystyle \frac{1}{(k(k+1))} = \frac{k}{k+1}$

now with k+1:

$\displaystyle \frac{1}{(k+1)(k+1+1)} = \frac{k+1}{k+1+1}$

$\displaystyle \frac{1}{(k+1)(k+2)} = \frac{k+1}{k+2}$

I don't really understand induction, I've looked up examples on google and such and I can't grasp it at all. I understand kind of how it works, but not how to do it.

A quick point in the right direction would be appreciated