The random variable X only accepts non-negative integer values. Prove that for any whole $2 \leq r $
$EX(X-1)...(X-r+1)=r\sum\limits_{n=1}^{\infty}n^{r-1}P\{{X > n \}}$
I tried to use this identity for a solution, but nothing worked
$EX=\sum\limits_{r=1}^{\infty}P\{{X\geq r\}}$
Also,i tried using genereting function $\phi(s)=\sum\limits_{n=1}^{\infty}s^nP\{{X=n\}}$,then $\phi^{(r)}(1)=EX(X-1)...(X-r+1)$, but that didn’t help either