> 
> **Possible Duplicate:**  
> 
> [proof by induction: n/(n+1)](https://math.stackexchange.com/questions/11831/proof-by-induction-n-n1) 
> 
> 
> 

Continuing from [here](https://math.stackexchange.com/a/134922/16797), I got a splendid answer that helped a lot. I'm tackling one now, but I've run into problems.

Prove by mathematical induction that

$$
\sum\_{r=1}^n \frac{1}{r(r+1)} = \frac{n}{n+1}
$$

Since I'm not all that conversant with Tex. . . I got to . . .

$$
\frac{2}{n(n+2)}
$$

How I got there is through fractional addition, expanding then factoring. I'm stuck now. 
Thanks. I would prefer simple answers.