Infinite product of consecutive odd/even, even/odd ratios


by Loren Booda
Tags: consecutive, even or odd, infinite, odd or even, product, ratios
Loren Booda
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#1
Sep16-09, 05:16 PM
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P: 3,408
[tex]?=\prod_{n=1}^\infty(n/(n+1))[/tex]
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CRGreathouse
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#2
Sep16-09, 05:35 PM
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Let
[tex]P(N)=\prod_{n=1}^N\frac{n}{n+1}.[/tex]

Then you're looking for [itex]\lim_{n\to\infty}P(n).[/itex]

P(1) = 1/2, P(2) = 1/2 * 2/3 = 1/3, P(3) = ... do you see what's going on here? What's the limit going to be?
rrronny
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#3
Sep16-09, 07:52 PM
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[tex]\lim_{N \to \infty}P(N) = \lim_{N \to \infty} \frac{1}{N+1} = 0.[/tex]

Loren Booda
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#4
Sep16-09, 10:02 PM
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Infinite product of consecutive odd/even, even/odd ratios


Thank you, CR. I just needed a little shaking up.


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