Results 1 to 3 of 3

Math Help - two series questions

  1. #1
    Newbie
    Joined
    Oct 2007
    Posts
    23

    two series questions

    Hi all,

    I had two questions

    1.  \sum ^{\infty}_{i=1} \frac{1}{\left(i-1\right)!} \frac{d}{d\lambda} \left(\lambda^{i}\right)= \frac{d}{d\lambda} \sum ^{\infty}_{i=1} \frac{1}{\left(i-1\right)!} \lambda^{i}


    2.  \sum^{\infty}_{x=1} x r^{x} = \frac{r}{\left(1-r\right)^{2}}

    why are 1 and 2 true
    For the first I think it has to do with the radius of convergence.

    Can someone help to prove this,

    Thank you very much
    Last edited by kuntah; February 26th 2008 at 10:32 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Peritus's Avatar
    Joined
    Nov 2007
    Posts
    397
    1. Power series - Wikipedia, the free encyclopedia

    2.


    \sum\limits_{x = 1}^\infty  {xr^x }  = r\sum\limits_{x = 1}^\infty  {xr^{x - 1}  = } r\sum\limits_{x = 1}^\infty  {\frac{d}<br />
{{dr}}r^x  = } r\frac{d}<br />
{{dr}}\sum\limits_{x = 1}^\infty  {r^x  = } r\frac{d}<br />
{{dr}}\frac{r}<br />
{{1 - r}} = \frac{r}<br />
{{\left( {1 - r} \right)^2 }}<br />
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2007
    Posts
    23
    thanks for the help

    I already solved the first now and thanks for the seccenodn )it was the same mechanism
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Series questions!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 29th 2011, 08:22 AM
  2. Power Series&Function Series Questions
    Posted in the Calculus Forum
    Replies: 10
    Last Post: January 19th 2010, 11:38 PM
  3. A series of questions...(1)
    Posted in the Advanced Algebra Forum
    Replies: 20
    Last Post: August 15th 2009, 12:54 AM
  4. series questions
    Posted in the Calculus Forum
    Replies: 0
    Last Post: March 17th 2009, 04:48 PM
  5. Series questions
    Posted in the Calculus Forum
    Replies: 26
    Last Post: June 2nd 2008, 02:23 PM

Search Tags


/mathhelpforum @mathhelpforum