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General Term of Binomial Expansion

If the 21st a...

Question

If the $21^{st}$ and $22^{nd}$ terms in the expansion of $(1 - x)^{44}$ are equal, then the value of $| 8 x |$ is

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Solution

Here, $T_{22} = T_{21}$
$\Rightarrow^{44} C_{21} (- x)^{21} =^{44} C_{20} (- x)^{20}$
$\Rightarrow \frac{^{44} C_{21}}{^{44} C_{20}} = \frac{1}{- x}$
$\Rightarrow \frac{44!}{21! \times 23!} \times \frac{20! \times 24!}{44!} = \frac{1}{- x}$
$\Rightarrow \frac{24}{21} = \frac{1}{- x}$
$\Rightarrow 8 x = - 7 \Rightarrow | 8 x | = 7$

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