The middle term in the expansion of x 2-1- x 2-2 n is-A- 2 n CnB- 2 -n Cn-2C- 2 n Cn-1D- 2 -2 n Cn-1

The correct option is A (x^2 + 1/x^2 + 2) = (x + 1/x)^2 Solution : (x^2 + 1/x^2 + 2) = (x + 1/x)^2 ⇒ (x^2 + 1/x^2 + 2)^n = (x + 1/x)^2n Since the power is a ...

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Standard XI

Mathematics

Middle Terms

The middle te...

Question

The middle term in the expansion of $(x^{2} + \frac{1}{x^{2}} + 2)^{n}$ is:

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Solution

The correct option is A

$(x^{2} + \frac{1}{x^{2}} + 2)$ = $(x + \frac{1}{x})^{2}$

Solution : $(x^{2} + \frac{1}{x^{2}} + 2)$ = $(x + \frac{1}{x})^{2}$

$\Rightarrow$ $(x^{2} + \frac{1}{x^{2}} + 2)^{n}$ = $(x + \frac{1}{x})^{2 n}$

Since the power is an even number, there will be only one middle term, which is $(\frac{2 n + 2}{2})^{t h}$ term or $(n + 1)^{t h}$ term.

$T_{n + 1} =^{2 n} C_{n} (x)^{n} (\frac{1}{x})^{n}$

= $^{2 n} C_{n}$

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Similar questions

The middle term in the expansion of $(x + \frac{1}{x})^{2 n}$ is:

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Q. Find the coefficient of

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The middle term in the expansion of (x2+1x2+2)n is:

The correct option is A (x2+1x2+2) = (x+1x)2 Solution : (x2+1x2+2) = (x+1x)2 ⇒ (x2+1x2+2)n = (x+1x)2n Since the power is an even number, there will be only one middle term, which is (2n+22)th term or (n+1)th term. Tn+1=2nCn(x)n(1x)n = 2nCn

The middle term in the expansion of $(x^{2} + \frac{1}{x^{2}} + 2)^{n}$ is: