Values of x for which a geometric series converges

[ellaingeborg]

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 :)

 

[Mark44]

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 :)

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

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