Question

To expand $(1 + 2x)^{- 1/2}$ as an infinite series, the range of x should be

• A. $\left\lbrack - \frac{1}{2},\frac{1}{2} \right\rbrack$
• B. $\left( - \frac{1}{2},\frac{1}{2} \right)$
• C. $\lbrack - 2,2\rbrack$
• D. (– 2, 2)

Answer 1

Answer: (B)

$\left( - \frac{1}{2},\frac{1}{2} \right)$

Answer 2

$(1 + 2x)^{- 1/2}$ can be expanded if $|2x| < 1$ i.e., if $|x| < \frac{1}{2}$ i.e.,

if $- \frac{1}{2} < x < \frac{1}{2}$ i.e., if $x \in \left( - \frac{1}{2},\frac{1}{2} \right)$.