Chapter 11.5, Problem 26E

To determine

Thefirst four terms in the Taylor series of $\frac{1}{\sqrt{1-x^2}}$ at $x=0$, where the Taylor series expansion $\frac{1}{\sqrt{1+x}}=1-\frac{1}{2}x+\frac{1\cdot 3}{2\cdot 4}{x}^2-\frac{1\cdot 3\cdot 5}{2\cdot 4\cdot 6}{x}^3+\frac{1\cdot 3\cdot 5\cdot 7}{2\cdot 4\cdot 6\cdot 8}{x}^4-\cdot \cdot \cdot$