Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

In this question,a proof using real analysis is given of the following identity: $$ \sum_{n=1}^{\infty} \frac{(n-1)!}{n \prod_{i=1}^{n} (a+i)} = \sum_{k=1}^{\infty} \frac{1}{(a+k)^2}$$

Is there a combinatorial proof of this identity? Is so, does the proof require that $a$ be a natural number? Also is there an easy way to verify if combinatorial proofs exist of particular identities?

share|cite|improve this question
I can answer the final question: No. –  Chris Godsil Dec 29 '12 at 5:05

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.