1 5 + 4x can be expanded by binomial theorem, if - Vidyadip

MCQ

$\frac{1}{{\sqrt {5 + 4x} }}$ can be expanded by binomial theorem, if

A
$x < 1$
B
$|x| < 1$
✓
$|x|\,\, < \frac{5}{4}$
D
$|x| < \frac{4}{5}$

✓

Answer

Correct option: C.

$|x|\,\, < \frac{5}{4}$

c
(c) The given expression can be written as ${5^{ - 1/2}}{\left( {1 + \frac{4}{5}x} \right)^{ - 1/2}}$and it is valid only when

$\left| {\frac{4}{5}x} \right| < 1$

$\Rightarrow |x| < \frac{5}{4}$

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