Closed form for infinite series $\sum_{n=1}^\infty \frac{1}{n(n+1)(n+2)\ldots(n+m)}$
Show that $\sum\limits_{k=1}^\infty \frac{1}{k(k+1)(k+2)\cdots (k+p)}=\frac{1}{p!p} $ for every positive integer $p$