An algebra problem by Pi Han Goh

Algebra Level 4

If A=n=11n(n+1)(n+2)(n+3)(n+4)(n+5), A = \displaystyle \sum_{n=1}^\infty \frac {1}{n(n+1)(n+2)(n+3)(n+4)(n+5)} , what is the value of 1A?\frac {1}{A}?

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