If third term in binomial expansion of {(1 + x)^m} is - frac{1}{8}{x^2} , then rational value of m i

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7.Binomial Theorem

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If the third term in the binomial expansion of ${(1 + x)^m}$ is $ - \frac{1}{8}{x^2}$, then the rational value of $m$ is

A

$2$

B

$1/2$

C

$3$

D

$4$

Solution

(b) We have ${(1 + x)^m} = 1 + mx + \frac{{m(m – 1)}}{{2!}}{x^2} + …$

By hypothesis, $\frac{{m(m – 1)}}{2}{x^2} = – \frac{1}{8}{x^2}$

==> $4{m^2} – 4m = – 1$

==> ${(2m – 1)^2} = 0$

$\Rightarrow m = \frac{1}{2}$.

Standard 11

Mathematics

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