Results 1 to 2 of 2

Math Help - Convergence proof 2...

  1. #1
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1

    Convergence proof 2...

    Check the convergence of:

    \Sigma _{n=0}^{\infty} \frac{1!+2!+...+n!}{(2n)!}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    Is...

    \frac{a_{n+1}}{a_{n}} = \frac{1! + 2! + \dots + (n+1)!}{(2n+2)!}\ \frac{(2n)!}{1! + 2! + \dots + n!} = \frac{1}{(2n+2)\ (2n+1)} \ \{1 + \frac{n+1}{1! + 2! + \dots + n!} \} (1)

    ... so that...

    \lim_{n \rightarrow \infty} \frac{a_{n+1}}{a_{n}} = 0 (2)

    ... and the series converges...

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Convergence proof
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: March 1st 2012, 04:48 PM
  2. Convergence Proof
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: October 12th 2009, 10:14 AM
  3. Proof of Convergence
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: August 17th 2009, 02:09 PM
  4. Convergence Proof
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 20th 2008, 12:16 PM
  5. Proof of Convergence
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 4th 2006, 10:29 AM

Search Tags


/mathhelpforum @mathhelpforum