use the geometric series formula $\frac{1}{1 - y}=sum_{n = 0}^{infty}y^{n}$ to express the function as a…

use the geometric series formula $\frac{1}{1 - y}=sum_{n = 0}^{infty}y^{n}$ to express the function as a series: $\frac{1}{1-sin^{3}x}=sum_{n = 0}^{infty}square$

use the geometric series formula $\frac{1}{1 - y}=sum_{n = 0}^{infty}y^{n}$ to express the function as a series: $\frac{1}{1-sin^{3}x}=sum_{n = 0}^{infty}square$

Answer

Explanation:

Step1: Identify substitution

Let $y = \sin^{3}x$.

Step2: Apply geometric - series formula

According to the geometric - series formula $\frac{1}{1 - y}=\sum_{n = 0}^{\infty}y^{n}$, substituting $y=\sin^{3}x$ gives $\frac{1}{1-\sin^{3}x}=\sum_{n = 0}^{\infty}(\sin^{3}x)^{n}=\sum_{n = 0}^{\infty}\sin^{3n}x$.

Answer:

$\sum_{n = 0}^{\infty}\sin^{3n}x$