Chapter 9.2, Problem 76E

Inverse sine Given the power series

$\frac{1}{\sqrt{1-x^2}}=1+\frac{1}{2}{x}^2+\frac{1\cdot 3}{2\cdot 4}{x}^4+\frac{1\cdot 3\cdot 5}{2\cdot 4\cdot 6}{x}^6+\cdot \cdot \cdot ,$

for −1 < x < 1, find the power series for f(x) = sin⁻¹ x centered at 0.