Question

${(1-x)}^{3/2}$ can be expanded in ascending powers of $x$ if

• A. $-1<x<1$
• B. $x<-1$
• C. $x>1$
• D. none of these

Answer 1

The correct option is A $-1<x<1$

Given, $(1-x{)}^{\frac{3}{2}}$
$=(1-x)\left[\sqrt{1-x}\right]$
Hence this can only be expanded in powers of x if
$|x|<1$
$\to -1<x<1$