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Homework Statement
Prove by induction the following summation formula:
[tex]\frac{1}{1\1*2} + \frac{1}{2*3} + ... + \frac{1}{n(n+1)} = 1  \frac{1}{n+1}[/tex]
[tex]n \geq 1[/tex]
Homework Equations

The Attempt at a Solution
Inductive step:
1. [tex]\frac{1}{1*2} + \frac{1}{2*3} + ... + \frac{1}{n(n+1)} + \frac{1}{(n+1)((n+1)+1)} = 1  \frac{1}{(n+1)+1}[/tex]
2. [tex]\frac{1}{1*2} + \frac{1}{2*3} + ... + \frac{1}{n(n+1)} + \frac{1}{(n+1)((n+1)+1)} = 1  \frac{1}{n+1} + \frac{1}{(n+1)(n+2)}[/tex]
To prove this (1) should equal (2) (right?), but I don't see how to manipulate (2) to make it equal to (1)
Thanks in advance!