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If the ratio of the coefficient of third and fourth term in the expansion of \left(x-\frac{1}{2 x}\right)^n is 1 : 2, then the value of n will be

Option: 1

18


Option: 2

16


Option: 3

12


Option: 4

-10


Answers (1)

best_answer

T_3={ }^n C_2(x)^{n-2}\left(-\frac{1}{2 x}\right)^2 \text { and } T_4={ }^n C_3(x)^{n-3}\left(-\frac{1}{2 x}\right)^3

But according to the equation

\frac{-n(n-1) \times 3 \times 2 \times 1 \times 8}{n(n-1)(n-2) \times 2 \times 1 \times 4}=\frac{1}{2} \Rightarrow n=-10

Posted by

Irshad Anwar

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