If up to infinitely many terms is equal to

MATHEMATICS · Single correct · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

1 + 2\sin x + 3\sin^2 x + 4\sin^3 x + \dots

up to infinitely many terms is equal to

4

, and the number of solutions of the equation in

\left[-\frac{3\pi}{2}, 4\pi\right]

k

, then the sum of all interior angles of a

k

-sided regular polygon is (1)

5\pi

(2)

4\pi

(3)

3\pi

(4)

2\pi