- #1
Benny
- 584
- 0
Hi, can someone tell me how I would go about evaluating the following infinite product? I've included the answer and it's taken from mathworld.
[tex]
\prod\limits_{n = 2}^\infty {\frac{{n^2 - 1}}{{n^2 + 1}}} = \pi \cos ech\left( \pi \right)
[/tex]
I think I'm supposed to be write an expression for the first n products and take the limit. I've tried doing that but I don't know what to do with the expression.
[tex]\left( {\frac{{2^2 - 1}}{{2^2 + 1}}} \right)\left( {\frac{{3^2 - 1}}{{3^2 + 1}}} \right)...\left( {\frac{{n^2 - 1}}{{n^2 + 1}}} \right)[/tex]
Any help would be good thanks.
[tex]
\prod\limits_{n = 2}^\infty {\frac{{n^2 - 1}}{{n^2 + 1}}} = \pi \cos ech\left( \pi \right)
[/tex]
I think I'm supposed to be write an expression for the first n products and take the limit. I've tried doing that but I don't know what to do with the expression.
[tex]\left( {\frac{{2^2 - 1}}{{2^2 + 1}}} \right)\left( {\frac{{3^2 - 1}}{{3^2 + 1}}} \right)...\left( {\frac{{n^2 - 1}}{{n^2 + 1}}} \right)[/tex]
Any help would be good thanks.