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

1. Sep 16, 2009

Loren Booda

$$?=\prod_{n=1}^\infty(n/(n+1))$$

2. Sep 16, 2009

CRGreathouse

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?

3. Sep 16, 2009

rrronny

$$\lim_{N \to \infty}P(N) = \lim_{N \to \infty} \frac{1}{N+1} = 0.$$

4. Sep 16, 2009

Loren Booda

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