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Math Help - Sum to Infinity of a Geometric Series

  1. #1
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    Sum to Infinity of a Geometric Series

    Q.: A geometric series has first term 1 and common ratio 1/2sin2(theta).

    (i) Find the sum of the first 10 terms when theta = pi/ 4, giving your answer in the form h - 1/2^k, where h, k E (i.e is a set of) N.

    (ii) Given that the sum to infinty is 4/3, find the value of theta if theta < 90 degrees.

    NB:I've already solved part (i), the jpg shows my attempt at part (ii).
    Ans.: From text book: 15 degrees.

    Sum to Infinity of a Geometric Series-maths-photo.jpg

    Thank you.
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    Re: Sum to Infinity of a Geometric Series

    \frac{1}{1 - \frac{1}{2}\sin(2t)} = \frac{4}{3}

    \frac{4}{4 - 2\sin(2t)} = \frac{4}{3}

    4-2\sin(2t) = 3

    \sin(2t) = \frac{1}{2}

    \sin(2t) = \sin(30^\circ)

    t = 15^\circ

    note that t = 75^\circ works also
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    Re: Sum to Infinity of a Geometric Series

    Thank you very much.
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