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

Loren Booda

[tex]?=\prod_{n=1}^\infty(n/(n+1))[/tex]

CRGreathouse

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

[tex]\lim_{N \to \infty}P(N) = \lim_{N \to \infty} \frac{1}{N+1} = 0.[/tex]

Loren Booda

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