1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Another Series problem

  1. Jul 31, 2007 #1
    1. The problem statement, all variables and given/known data

    Why does sin(x) - 1/2sin^2(x) + 1/4sin^3(x) - 1/8 sin^4(x) + ... = 2sin(x)/2+sin(x)

    How do you know for certain the series converges for all real values of x?

    2. Relevant equations

    3. The attempt at a solution

    Have no clue where to even start...

    Thanks for any help...
  2. jcsd
  3. Jul 31, 2007 #2
    You should use the standard series identity

    [tex]\sum_{n=0}^{\infty} y^n = \frac{1}{1-y}[/tex]

    The series converges for |y|<1. With an appropriate substitution you can make this series appear in your problem.
  4. Aug 1, 2007 #3


    User Avatar
    Science Advisor

    You might want to consider, separately, what happens when x= [itex]\pi/2[/itex]or x= [itex]-\pi/2[/itex].
  5. Aug 2, 2007 #4

    Gib Z

    User Avatar
    Homework Helper

    To make dhris's hint more obvious, just show that

    [tex]\sum_{n=0}^{\infty} (\frac{- \sin x}{2})^n = \frac{2}{2+ \sin x}[/tex]
    then multiply through out by sin x.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook