I found this problem recently on Yahoo Answers! It is gone now because it went unanswered after four days, and it is the policy of YA! to delete such questions.

Given:

Prove:

, for all natural numbers . (Since "natural number" is ambiguous, let's say for non negative—or possibly positive integers.)

I couldn't get passed the singularities at and . WolframAlpha couldn't provide an answer either, even for (e.g.), .

I have my doubts about this being true; however, if it is I would like to see a proof.