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## Homework Statement

given a geometric sequence sin(x),sin(2x), . . .

c) find for which values of x∈(0,π) this sequence converges and calculate its limit

## Homework Equations

|q|<1 or -1<q<1

## The Attempt at a Solution

Ok so in part a) and b) i calculated the quotient and found out that

q=sin2x/sinx

q=(2*cos(x)*sin(x))/(sin(x))

q=2*cos(x)

so know i tried to figure out for which values x will converge

|q|<1

-1<q<1

-1<2*cos(x)<1 /:2

-1/2<cos(x)<1/2

2π/3>x>π/3

which means that the sequence will converge when the angle is anywhere between 120° and 60°

However i'm unsure now how to continue to find the limit because I've never seen an example where the value x isin't exactly defined

could someone show me how this is done or give me some kind of a hit or check if I made a mistake somewhere inbetween

Thanks

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