Results 1 to 2 of 2

Math Help - Geometric Progression - Sum it upto n-terms

  1. #1
    Newbie
    Joined
    Feb 2010
    From
    Near Chennai
    Posts
    20

    Question Geometric Progression - Sum it upto n-terms

    Sum the series upto n-terms : 1+(1+x)+(1+x+x^2)+(1+x+x^2+x^3)...............

    Answer in the book is [n/(1-x)] - [x(1-x)^n / (1-x)^2]

    The answer is in the book, but i dont know how to find it. I need the full solution for the problem by step by step. Can you please anybody give me help to solve this?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    The sum can be written as
    \displaystyle\sum_{k=0}^{n-1}(1+x+x^2\ldots+x^k)=\displaystyle\sum_{k=0}^{n-1}\frac{1-x^{k+1}}{1-x}=

    =\displaystyle\sum_{k=0}^{n-1}\frac{1}{1-x}-\displaystyle\sum_{k=0}^{n-1}\frac{x^{k+1}}{1-x}=\frac{n}{1-x}-\frac{x(1-x^{n})}{(1-x)^2}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: February 8th 2011, 02:28 PM
  2. number of terms in geometric progression
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: December 8th 2010, 12:55 PM
  3. Arithmetic progression and ratio of terms.
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: March 10th 2010, 11:19 AM
  4. Geometric Progression or Geometric Series
    Posted in the Math Topics Forum
    Replies: 8
    Last Post: October 8th 2009, 07:31 AM
  5. Replies: 8
    Last Post: March 23rd 2009, 07:26 AM

Search Tags


/mathhelpforum @mathhelpforum