Prove that:

$\displaystyle \sum_{i=4}^{\infty} \frac{2}{i(i-1)(i-2)(i-3)} = \frac{1}{3}$

I think I'm supposed to use the fact that any decreasing sequence $\displaystyle a_1 \dots a_n $ can be written as:

$\displaystyle a_n-a_1 = (a_n - a_{n+1}) + \dots (a_3 - a_2) + (a_2 - a_1)$