Question

This series converges to .........\[\sum_{n=1}^{\infty}(-\frac{ 1 }{ 2 })^{n-1}\sin^{n}(x)\]

Answer 1

\[= sinx( 1 - sinx/2 + (-sinx/2)^2 + (-sinx/2)^3 ...............)\]

Answer 2

Try using formula for an infitnite GP with common ratio -sinx/2 from here :)

Answer 3

You'll get te answer :D