Results 1 to 2 of 2

Thread: find the sum of the series

  1. #1
    Newbie
    Joined
    Mar 2010
    From
    Agartala, India
    Posts
    3

    find the sum of the series

    Find the sum of the series $\displaystyle \sum_{n = 1}^\infty \frac{{-1}^{n }*{4}^{n } }{ n! n}$
    Last edited by topsquark; May 12th 2011 at 05:13 PM. Reason: Fixed LaTeX code
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,163
    Thanks
    46
    Quote Originally Posted by jayantamath View Post
    Find the sum of the series $\displaystyle \sum_{n = 1}^\infty \frac{{-1}^{n }*{4}^{n } }{ n! n}$

    If you mean

    $\displaystyle \sum_{n=1}^{+\infty}\dfrac{(-1)^n4^n}{n!n}$

    then, consider the functional series

    $\displaystyle f(x)=\sum_{n=1}^{+\infty}\dfrac{(-1)^nx^n}{n!n}$

    $\displaystyle f'(x)=\dfrac{1}{x}\sum_1^{+\infty}\dfrac{(-1)^nx^n}{n!}=\dfrac{e^{-x}-1}{x}$

    You'll obtain

    $\displaystyle f(4)=\textrm{Ei}(-4)-\gamma-\log 4$

    where

    $\displaystyle \textrm{Ei}(x)=-\int_{-x}^{+\infty}\dfrac{e^{-t}dt}{t}$

    and $\displaystyle \gamma$ the Euler-Mascheroni constant.
    Last edited by FernandoRevilla; May 13th 2011 at 01:31 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: Sep 29th 2010, 06:11 AM
  2. find the sum of the series
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Mar 28th 2010, 09:43 PM
  3. Binomial Series to find a Maclaurin Series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Jul 21st 2009, 07:15 AM
  4. Find sum of the following series?
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: Apr 27th 2009, 09:23 PM
  5. find the value of the p series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Apr 10th 2007, 04:45 PM

Search Tags


/mathhelpforum @mathhelpforum