Infinite summation

If $\displaystyle \sum_{n=1}^\infty \dfrac1{n(n+1)(n+2)\cdots (n+6)} = \dfrac1a$ , find $\dfrac a6$ .

Hint : Generalize it for $\displaystyle \sum_{n=1}^\infty \dfrac1{n(n+1)(n+2)\cdots(n+k)}$ .