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

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

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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
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@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
    
@CliveNewstead There's nothing like that. You are completely going out of the way. Thats the same for Ron Gordon too. –  Lakshay Goel Apr 8 '13 at 14:19
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@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
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marked as duplicate by Cameron Buie, azimut, Dominic Michaelis, Martin, Davide Giraudo Apr 8 '13 at 15:14

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1 Answer

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

You'll see that terms cancel out each other .

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