# Math Help - Sum to Infinity of a Geometric Series

1. ## 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.

Thank you.

2. ## 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

3. ## Re: Sum to Infinity of a Geometric Series

Thank you very much.