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AP® Calculus AB-BC

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Convergence of a Trigonometric Sum

APCALC-BJBCUE

For which values of $x$ on the interval $(0, \pi)$ will the series below converge?

$$\sum _{ n=1 }^{ \infty }{ ( \sin { x } ) ^{ n } } $$

A

$ (0, \pi)$

B

$(0,\cfrac{\pi}{2})$ or $(\cfrac{\pi}{2},\pi)$

C

$ (0, \cfrac{\pi}{2})$

D

$ (\cfrac{\pi}{2},\pi )$