The greatest coefficient in the expansion of x -1- x 2 nA- 2 n -n-2 -2B- None of these 2 n -C-D- n - n -n - 2n

The correct option is C 2n!n!n!The total number of terms in the expansion of nbsp;(x+1/x nbsp; )^ 2n is 2n+1 i.e. there are total odd number of terms. nb ...

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Standard XII

Mathematics

Middle Terms

The greatest ...

Question

The greatest coefficient in the expansion of $(x + \frac{1}{x})^{2 n}$ is

\frac{1.3.5.... (2 n - 1)}{n!} 2^{n}

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\frac{2 n!}{n! n!}

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\frac{2 n!}{{(\frac{n}{2}!)}^{2}}

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None of these

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Solution

The correct option is B $\frac{2 n!}{n! n!}$
The total number of terms in the expansion of $(x + \frac{1}{x})^{2 n}$ is $2 n + 1$ i.e. there are total odd number of terms.

The greatest coefficient in the expansion is that of the middle term
The coefficient of the middle term is,
$=^{2 n} C_{n} = \frac{2 n!}{n! n!}$

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Similar questions

Q. The Greatest co-efficient in the expansion of

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(a)

\frac{n!}{[(n - 1)! (n + 1)!]}

(b)

\frac{(2 n)!}{[(n - 1)! (n + 1)!]}

(c)

\frac{(2 n)!}{(2 n - 1)! (2 n + 1)!}

(d) none of these

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Q. If

^{2 n} C_{6}

is the greatest coefficient in the expansion of

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then

n

bino is

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The greatest coefficient in the expansion of (x+1x)2n is

The correct option is B 2n!n!n!The total number of terms in the expansion of (x+1x)2n is 2n+1 i.e. there are total odd number of terms. The greatest coefficient in the expansion is that of the middle term The coefficient of the middle term is, = 2nCn=2n!n!n!

The greatest coefficient in the expansion of $(x + \frac{1}{x})^{2 n}$ is