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!

Homework Help: Finding x in a geometric progression, given the sum.

  1. Sep 14, 2010 #1
    1. The problem statement, all variables and given/known data

    If

    [tex]1 + 2x + 4x^2 + ... = \frac{3}{4}[/tex]

    find the value of x. [Edit: Forgot to ask the question]

    2. Relevant equations

    [tex]S_n = \frac{a(1 - r^n)}{1 - r} [/tex]

    [tex] t_n = ar^{n-1} [/tex]

    3. The attempt at a solution

    a = 1

    r = 2x

    I try to solve [tex]S_n[/tex] and end up with

    [tex]2x^n = \frac{6x - 7}{4}[/tex]

    which I can't solve.

    I try to solve by equating t2 and t3 and getting x = (1/2). Which is wrong.

    Any help appreciated.
     
    Last edited: Sep 15, 2010
  2. jcsd
  3. Sep 14, 2010 #2
    Is the sum is to infinity?
    or to 'n terms'?

    If it is to infinity, Apply limit to your equation.
     
  4. Sep 14, 2010 #3

    HallsofIvy

    User Avatar
    Science Advisor

    If this is an infinite sum the formula is
    [tex]S_\infty= \frac{a}{1- r}[/tex]

    If it is a finite sum, you would need to know how many terms so that "n" would be an actual integer, not a variable.

    The "..." at the end of the sum indicates it is an infinite sum.

     
  5. Sep 15, 2010 #4
    I've edited the original post. The problem is to find the value of x.

    Its not an infinite sum. The only solution I can see is to solve for n in the infinite series and the summation, and try to solve simultaneously.
     
  6. Sep 15, 2010 #5
    I had to read your answer a couple of times. I get it now. Its an infinite sum. No powers to work out.

    Thank you so much.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook