Prove Without Induction: $\sum\limits_{k=2}^{n} \frac{1}{k(k-1)} = 1 - \frac{1}{n}$ everybody.
I'm suppose to prove this without induction:
Prove Without Induction: $\sum\limits_{k=2}^{n} \frac{1}{k(k-1)} = 1 - \frac{1}{n}$
I'm not sure how to do it. I tried a bit of algebraic manipulation, but I'm not sure how to do it.
It's suppose to be basic. 
I did get a hint of factorizing $\frac{1}{k(k-1)}$ but that didn't get me anywhere.
A hint or any directions would be much appreciated!

That's a telescoping series. Use partial fraction techniques to do the following split: $$\frac{1}{k(k-1)} = \frac{1}{k-1} - \frac{1}{k},$$ and proceed from there.
