Results 1 to 4 of 4

Math Help - Absolute convergence of a Serie

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    87

    Absolute convergence of a Serie

    Determine whether the series is absolutely convergent.

    the series from 1 to infinity of

    10^n/((n+1)4^(2n+1))
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by amiv4 View Post
    Determine whether the series is absolutely convergent.

    the series from 1 to infinity of

    10^n/((n+1)4^(2n+1))
    There is no alternating term here, so obviously if this fails to converge it does not converge absolutely.

    Note \sum_{n=1}^{\infty}\frac{10^n}{(n+1)4^{2n+1}}=\sum  _{n=1}^{\infty}\frac{10^n}{4(n+1)16^n}\leq\sum_{n=  1}^{\infty}\left(\frac{10}{16}\right)^n=\frac{8}{3  }
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2008
    Posts
    87
    I'm not seeing what you did when u changed the original problem to that equation with the 16^n on the bottom. could u explain how u got that
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by amiv4 View Post
    I'm not seeing what you did when u changed the original problem to that equation with the 16^n on the bottom. could u explain how u got that
    4^{2n+1}=4\cdot{4^{2n}}=4\cdot\left(4^2\right)^n=4  \cdot{16^n}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: March 3rd 2011, 11:55 PM
  2. [SOLVED] iterating weighted serie to convergence
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: March 3rd 2011, 09:35 PM
  3. Convergence of a serie.
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 9th 2011, 01:53 PM
  4. Absolute Convergence
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 6th 2008, 10:50 PM
  5. absolute convergence
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 26th 2007, 06:04 PM

Search Tags


/mathhelpforum @mathhelpforum