# Calculate the product $\prod_{n=2}^\infty \frac{n^3-1}{n^3+1}$ [duplicate]

I'm not sure where to begin in calculating the following product. Can anyone help me?

$$\prod_{n=2}^{\infty}\dfrac{n^3-1}{n^3+1}$$

Waiting for replies!

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## marked as duplicate by Cameron Buie, azimut, Dominic Michaelis, Martin, Davide GiraudoApr 8 '13 at 15:14

Show us what you've tried and/or what your thoughts are about how you'd go about solving the problem. "Answer it fast" makes me suspicious that this is graded homework... –  Clive Newstead Apr 8 '13 at 14:14
@CliveNewstead: or that he's in that he's in the middle of an exam. Perhaps the OP will learn that asking us to "answer it fast" will make us not want to answer it at all. –  Ron Gordon Apr 8 '13 at 14:16
I think this is a duplicate but I can't seem to find it. –  Ishan Banerjee Apr 8 '13 at 14:17
@LakshayGoel: Be that as it may, I'd be willing to help if you showed some of your working or thoughts on the matter, then I'd have an idea of how best to explain it without just writing down the solution in full. If you give some working then I'll happily retract my downvote. –  Clive Newstead Apr 8 '13 at 14:22
@RonGordon: if he is in the middle of an exam and has online access, I would advice to use wolfram alpha for such type of questions ;-) –  Fabian Apr 8 '13 at 14:59

Write a few terms of the product after factorizing it as $\frac{(n-1)(n^2+n+1)}{(n+1)(n^2-n+1)}$..