Question

Solve this $(1+x{)}^{\frac{1}{2}}$

Answer 1

For fractional powers,

${(1+x)}^n=1+nx+\frac{n(n-1)}{2!}{x}^2+\frac{n(n-1)(n-2)}{3!}{x}^3+.....$

$\therefore {(1+x)}^{1/2}=1+\frac{x}{2}+\frac{\frac{1}{2}\left[\frac{-1}{2}\right]}{2!}{x}^2+\frac{\frac{1}{2}\left(\frac{-1}{2}\right)\left(\frac{-3}{2}\right)}{3!}{x}^3+....$

$=1+\frac{x}{2}+\left(\frac{-1}{16}\right)x^2+\frac{3}{48}{x}^3+...$