1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sum to Infinity of a Geometric Series

  1. Aug 13, 2011 #1
    1. The problem statement, all variables and given/known data

    Q. Find, in terms of x, the sum to infinity of the series...

    1 + [itex](\frac{2x}{x + 1})[/itex] + [itex](\frac{2x}{x + 1})^2[/itex] + ...

    2. Relevant equations

    S[itex]\infty[/itex] = [itex]\frac{a}{1 - r}[/itex]

    3. The attempt at a solution

    S[itex]\infty[/itex] = [itex]\frac{a}{1 - r}[/itex]

    a = 1

    r = U2/ U1 = [itex](\frac{2x}{x + 1})[/itex]/ 1 = [itex]\frac{2x}{x + 1}[/itex]

    [itex]\frac{1}{1 - (2x/ x + 1)}[/itex]

    [itex]\frac{x + 1}{1 - 2x}[/itex]

    Ans.: From text book: [itex]\frac{x + 1}{1 - x}[/itex]

    Can anyone help me figure out where the 2x becomes just x? Thank you.
  2. jcsd
  3. Aug 13, 2011 #2


    User Avatar
    Homework Helper

    If you take

    [tex]\frac{1}{x-\frac{2x}{x+1}} \times \frac{x+1}{x+1}[/tex]

    you will get


    Which simplifies to the answer you want.
  4. Aug 13, 2011 #3
    Thanks for clearing that up. I appreciate the help.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Sum to Infinity of a Geometric Series