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

$$?=\prod_{n=1}^\infty(n/(n+1))$$
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 Recognitions: Homework Help Science Advisor Let $$P(N)=\prod_{n=1}^N\frac{n}{n+1}.$$ Then you're looking for $\lim_{n\to\infty}P(n).$ 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?
 $$\lim_{N \to \infty}P(N) = \lim_{N \to \infty} \frac{1}{N+1} = 0.$$

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

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