If the ratio of the coefficient of third and fourth term in the expansion of x-1-2 xn is 1- 2- then the value of n will beA- 18B- 12C- 16D- -10

The correct option is D 10 T_3 = ^n C _2(x)^n 2( 1/2x)^2 and T_4 = ^n C _3(x)^n 3( 1/2x)^3 But according to the condition, n(n 1)×3×2×1×8/n(n 1)(n 2)×2×1×4 = ...

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Standard XI

Mathematics

General Term of Binomial Expansion

If the ratio ...

Question

If the ratio of the coefficient of third and fourth term in the

expansion of $(x - \frac{1}{2 x})^{n}$ is 1:2, then the value of n will be

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-10

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Solution

The correct option is D
-10

$T_{3}$ = $^{n} C_{2}$ $(x)^{n - 2}$ $(- \frac{1}{2 x})^{2}$ and $T_{4}$ = $^{n} C_{3}$ $(x)^{n - 3}$ $(- \frac{1}{2 x})^{3}$

But according to the condition,

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

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