Results 1 to 5 of 5

Math Help - Convergence of a Series

  1. #1
    Newbie
    Joined
    Feb 2011
    Posts
    13

    Convergence of a Series

     (2^x+9^x)/18^x

    I have to find the sum of this series from x=1 to infinity, which means that it is either a telescoping or a geometric series. I can't choose which because of its awkward format.
    I know that it converges, but I don't what it converges to. Please don't give me the answer. I would just like a hint or a first step of what to do.

    I've already tried this:

     (2^x+9^x)/18^x = (1/9)^x+(1/2)^x
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    Use:

    \displaystyle\sum_{x=0}^{+\infty}r^x=\dfrac{1}{1-r},\quad (|r|<1)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2011
    Posts
    13
    So it's a geometric series. Should I find the sum of the (1/9)^x and (1/2)^x and just add them together?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Ted
    Ted is offline
    Member
    Joined
    Feb 2010
    From
    China
    Posts
    199
    Thanks
    1
    ^^
    Yes.
    But becareful, the formula in post#2 is used when the sums starts with x=0.

    The actual formula is S=\dfrac{a}{1-r} where a = first term, r = ratio. and |r| must be < 1.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    Quote Originally Posted by JewelsofHearts View Post
    So it's a geometric series. Should I find the sum of the (1/9)^x and (1/2)^x and just add them together?

    Use the theorem:

    \sum_{n=1}^{+\infty}u_n,\; \sum_{n=1}^{+\infty}v_n both convergent with sums U,V respectively, then \sum_{n=1}^{+\infty}(u_n+v_n) (sum series) is convergent with sum U+V .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: October 3rd 2011, 01:12 AM
  2. Replies: 2
    Last Post: May 1st 2010, 09:22 PM
  3. Replies: 4
    Last Post: December 1st 2009, 03:23 PM
  4. Replies: 3
    Last Post: December 1st 2009, 03:06 PM
  5. series convergence and radius of convergence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 15th 2008, 08:07 AM

Search Tags


/mathhelpforum @mathhelpforum