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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


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    Staff Emeritus
    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.
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