# Help with induction proof

1. Feb 27, 2012

### thefeedinghan

Hello there, I'm having trouble proving this by induction

1. The problem statement, all variables and given/known data
$\frac{1}{1(2)} + 1\frac{1}{2(3)}+...+\frac{1}{n(n+1)} = \frac{n}{n+1}$

2. Relevant equations
For the base case n=1

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

$\frac{k}{k+1} + \frac{1}{(k+1)(k+2)}$ <- the second term would be the next integer
3. The attempt at a solution
$\frac{1}{1(2)}+ \frac{1}{2(3)}+\frac{1}{k(k+1)} + \frac{1}{(k+1)(k+2)} = \frac{k+1}{(k+1)+1} = \frac{k}{k+2} + \frac{1}{k+2}$

I don't know where to go from here, any help would be appreciated

2. Feb 27, 2012

### tiny-tim

welcome to pf!

hi welcome to pf!
ok, now put the whole thing over (k+1)(k+2) …

what do you get?

3. Feb 27, 2012

### thefeedinghan

oh, thanks very much! was pretty obvious now!