Results 1 to 7 of 7

Math Help - limiting sum of a series??

  1. #1
    Member
    Joined
    Aug 2009
    Posts
    96

    limiting sum of a series??

    the limiting sum of 3 + x + x^2 + ..... is 18. If |x|<1, find x
    how do you do this??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7
    Quote Originally Posted by deej813 View Post
    the limiting sum of 3 + x + x^2 + ..... is 18. If |x|<1, find x
    how do you do this??
    3+x+x^2+...=18

    3+\frac{x}{1-x}=18

    \frac{x}{1-x}=15

    x=15-15x

    16x=15

    x=\frac{15}{16}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Aug 2009
    Posts
    96
    how does that work??
    where does the x/1-x come from??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,553
    Thanks
    1423
    Everything after the 3 is an infinite geometric series.

    For any infinite geometric series of the form

    S_n = a + ar + ar^2 + ar^3 + \dots

    converges to \frac{a}{1 - r}, provided |r| < 1.


    In your case, the infinite geometric series is

    S_n = x + x^2 + x^3 + x^4 + \dots.


    Can you see what a and r have to be?

    Can you see what it converges to if |x| < 1?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Aug 2009
    Posts
    96
    wouldn't it be 3/1-x cos isn't a=3??
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,553
    Thanks
    1423
    No.

    I said the terms AFTER the 3.


    In other words, your equation is

    3 + \left(x + x^2 + x^3 + \dots\right) = 18.


    We are only dealing with the stuff inside the brackets.


    Edit: It might help if you subtract the 3 to the other side.

    So the equation becomes

    x + x^2 + x^3 + \dots = 15.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Aug 2009
    Posts
    96
    oh ok i get it
    thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Limiting
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: July 9th 2010, 10:15 AM
  2. Limiting parallels
    Posted in the Geometry Forum
    Replies: 1
    Last Post: April 4th 2010, 10:17 PM
  3. [SOLVED] Limiting Sum of Geometric Series
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 30th 2010, 01:38 AM
  4. What are the Limiting Distribution and Limiting Probabilities
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: April 3rd 2009, 12:49 PM
  5. Series problem with limiting sum
    Posted in the Algebra Forum
    Replies: 3
    Last Post: June 8th 2007, 06:39 AM

Search Tags


/mathhelpforum @mathhelpforum