Question

Find the Maclaurin series in closed form of f(x)=(1)/(sq rt (1-x))

Answer 1

maclarin series is..
\[f(x)=f(0)+f'(0)x+f''(0)\frac{x^2}{2!}+f'''(0)\frac{x^3}{3}+f^{(4)}(0)\frac{x^4}{4!}+ \cdots +f^{(n)}(0)\frac{x^n}{n!}+ \cdots \]

Answer 2

\[f(x)=\frac{1}{\sqrt{x-1}}, f(0)=\frac{1}{\sqrt{1-0}}=\frac{1}{1}=1\]
\[f(x)=(1-x)^\frac{-1}{2}, f'(x)=\frac{-1}{2}(1-x)^{\frac{-1}{2}-1}(-1)=\frac{1}{2}(1-x)^\frac{-3}{2}\]
\[f'(0)=\frac{1}{2}\]
\[f''(x)=\frac{1(-3)}{2(2)}(1-x)^{\frac{-3}{2}-1}\]

Answer 3

so on...

Answer 4

Thank you very much