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(B) The binomial expansion of $(1 + x)^m$ is given by $1 + mx + \frac{m(m - 1)}{2!}x^2 + \dots$According to the problem,the third term is $\frac{m(m -

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$1/2$

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(B) The binomial expansion of $(1 + x)^m$ is given by $1 + mx + \frac{m(m - 1)}{2!}x^2 + \dots$According to the problem,the third term is $\frac{m(m - 1)}{2}x^2 = -\frac{1}{8}x^2$.Equating the coefficients,we get $\frac{m(m - 1)}{2} = -\frac{1}{8}$.Multiplying both sides by $8$,we get $4m(m - 1) = -1$.$4m^2 - 4m + 1 = 0$.This is a perfect square: $(2m - 1)^2 = 0$.Therefore,$2m - 1 = 0$,which gives $m = \frac{1}{2}$.

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

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