1. PF Insights is off to a great start! Fresh and interesting articles on all things science and math. Here: PF Insights

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

  1. [tex]?=\prod_{n=1}^\infty(n/(n+1))[/tex]
     
  2. jcsd
  3. CRGreathouse

    CRGreathouse 3,682
    Science Advisor
    Homework Helper

    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?
     
  4. [tex]\lim_{N \to \infty}P(N) = \lim_{N \to \infty} \frac{1}{N+1} = 0.[/tex]
     
  5. Thank you, CR. I just needed a little shaking up.
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?
Similar discussions for: Infinite product of consecutive odd/even, even/odd ratios
Loading...