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Values of x for which a geometric series converges

  1. Apr 6, 2017 #1
    Need help with a homework question!
    The question gives: The first three terms of a geometric sequence are sin(x), sin(2x) and 4sin(x)cos^2(x) for -π/2 < x < π/2.
    First I had to find the common ratio which is 2cos(x)
    Then the question asks to find the values of x for which the geometric series sinx + sin2x + ... converges.
    I am not sure how to go about this question.
    I tried using
    S∞= u/(1-r) where r is the common ratio, u is the first term of the sequence and S∞ the sum of the series.
    this sum would equal
    sinx/(1-2cosx)

    Please help! My finals are coming up and I need to know this thank you :)
     
  2. jcsd
  3. Apr 6, 2017 #2

    Mark44

    Staff: Mentor

    A geometric series converges if |r| < 1. What does this mean in relation to your geometric series?

    In the future, please do not delete the three parts of the homework template. It is required for homework questions.
     
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