Results 1 to 2 of 2

Math Help - Series Converge or diverge 2

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    3

    Series Converge or diverge 2

    consider the series
    (1+1) + (0.3-.4642) + (0.03 + .2154) + (0.003 - .1000) + (.0003 + .0464) + ..........

    I found the series to be:

     \Sigma_{n=0}^{\infty} {3(1/10)^n} + (-1)^{n+1}(1/\sqrt[3]{10})^n<br />

    I found it to be convergent because 3\Sigma_{n=0}^{\infty} (1/10)^n converges by geometric series test because r= |1/10| < 1

    and

    \Sigma_{n=0}^{\infty} (-1)^{n+1}(1/\sqrt[3]{10})^n

    converges by geometric series test becuse the |r| < 1 also

    so...
    the series

    \Sigma_{n=0}^{\infty} {3(1/10)^n} + (-1)^{n+1}(1/\sqrt[3]{10})^n


    would convergem but then I have to find the EXACT sum of the series and I don't know how to do this.
    Last edited by badBKO; November 23rd 2008 at 07:55 PM.
    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 badBKO View Post
    consider the series
    (1+1) + (0.3-.4642) + (0.03 + .2154) + (0.003 - .1000) + (.0003 + .0464) + ..........

    I found the series to be:

     \Sigma_{n=0}^{\infty} {3(1/10)^n} + (-1)^{n+1}(1/\sqrt[3]{10})^n<br />

    I found it to be convergent because 3\Sigma_{n=0}^{\infty} (1/10)^n converges by geometric series test because r= |1/10| < 1

    and

     <br />
\Sigma_{n=0}^{\infty} (-1)^{n+1} (1/\sqrt[3]{10})^n<br />
    converges by geometric series test becuse the |r| < 1 also

    so...
    the series
    math]
    \Sigma_{n=0}^{\infty} {3(1/10)^n} + (-1)^{n+1}(1/\sqrt[3]{10})^n
    [/tex]

    would convergem but then I have to find the EXACT sum of the series and I don't know how to do this.
    \sum_{n=0}^{\infty}\left\{3\left(\frac{1}{10}\righ  t)^n-\left(\frac{-1}{\sqrt[3]{10}}\right)^n\right\}

    You chould know that \forall{x}\backepsilon|x|<1~\sum_{n=0}^{\infty}x^n  =\frac{1}{1-x}

    So your sum is \frac{3}{1-\frac{1}{10}}-\frac{1}{1+\frac{1}{\sqrt[3]{10}}}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Does this series converge or diverge?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 6th 2010, 10:15 AM
  2. Series: Converge of Diverge
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: May 6th 2010, 05:05 AM
  3. Does this series converge or diverge?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 30th 2009, 08:57 AM
  4. Series help!; converge or diverge
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 23rd 2008, 06:19 PM
  5. Series converge or diverge?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 1st 2008, 09:12 AM

Search Tags


/mathhelpforum @mathhelpforum