(B) The binomial expansion of $(1 + y)^n$ is valid for $|y| < 1$.Here,$y = 2x$ and $n = -1/2$.For the series to be convergent,we must have $|2x| < 1$.

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(B) The binomial expansion of $(1 + y)^n$ is valid for $|y| Here,$y = 2x$ and $n = -1/2$.For the series to be convergent,we must have $|2x| This implies $|x| Therefore,the range of $x$ is $-1/2 < x < 1/2$,which can be written as $x \in ( -1/2, 1/2 )$.

Class 11 Mathematics Binomial Theorem Binomial theorem for any index

Medium

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

A
$[ -1/2, 1/2 ]$
B
$( -1/2, 1/2 )$
C
$[ -2, 2 ]$
D
$( -2, 2 )$

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Class 11

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Binomial Theorem

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Binomial theorem for any index

The expression $\frac{1}{(x^2 + \frac{1}{x})^{4/3}}$ can be expanded by the binomial theorem if:

Easy

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If $|x| > 1$,then $(1 + x)^{-2} = $

Difficult

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$\frac{1}{8} - \frac{7}{8 \times 12} + \frac{7 \times 10}{8 \times 12 \times 16} - \ldots =$

DifficultTS EAMCET 2022

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The sum of the series $\frac{3}{4 \cdot 8}-\frac{3 \cdot 5}{4 \cdot 8 \cdot 12}+\frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12 \cdot 16}-\ldots$

DifficultAP EAMCET 2007

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If $(a+bx)^{-3} = \frac{1}{27} + \frac{1}{3}x + \dots$,then the ordered pair $(a, b)$ is equal to

EasyAP EAMCET 2014

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

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The expression $\frac{1}{(x^2 + \frac{1}{x})^{4/3}}$ can be expanded by the binomial theorem if:

If $|x| > 1$,then $(1 + x)^{-2} = $

$\frac{1}{8} - \frac{7}{8 \times 12} + \frac{7 \times 10}{8 \times 12 \times 16} - \ldots =$

The sum of the series $\frac{3}{4 \cdot 8}-\frac{3 \cdot 5}{4 \cdot 8 \cdot 12}+\frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12 \cdot 16}-\ldots$

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