(B) Let the coefficients of two consecutive terms be $^nC_r$ and $^nC_{r+1}$.Given that $^nC_r = ^nC_{r+1}$.Using the formula $^nC_r = \frac{n!}{r!(n-

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(B) Let the coefficients of two consecutive terms be $^nC_r$ and $^nC_{r+1}$.Given that $^nC_r = ^nC_{r+1}$.Using the formula $^nC_r = \frac{n!}{r!(n-r)!}$,we have:$\frac{n!}{r!(n-r)!} = \frac{n!}{(r+1)!(n-r-1)!}$$\frac{1}{r!(n-r)(n-r-1)!} = \frac{1}{(r+1)r!(n-r-1)!}$$\frac{1}{n-r} = \frac{1}{r+1}$$r + 1 = n - r$$n = 2r + 1$Since $r$ is an integer,$2r + 1$ is always an odd integer. Therefore,$n$ must be an odd integer.

Class 11 Mathematics Binomial Theorem General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

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The coefficients of two consecutive terms in the expansion of $(1 + x)^n$ will be equal,if

A
$n$ is any integer
B
$n$ is an odd integer
C
$n$ is an even integer
D
None of these

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Binomial Theorem

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General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

The coefficient of $x^3$ in the expansion of $(x - \frac{1}{x})^7$ is

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The term independent of $x$ in ${\left[ {\sqrt{\frac{x}{3}} + \frac{{\sqrt{3}}}{{{x^2}}}} \right]^{10}}$ is

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If for positive integers $r > 1$ and $n > 2$,the coefficients of the $(3r)^{th}$ and $(r + 2)^{th}$ powers of $x$ in the expansion of $(1 + x)^{2n}$ are equal,then:

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Find $a$ if the coefficients of $x^{2}$ and $x^{3}$ in the expansion of $(3+ax)^{9}$ are equal.

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The number of integral terms in the expansion of $(5^{\frac{1}{2}} + 7^{\frac{1}{8}})^{1016}$ is

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The coefficients of two consecutive terms in the expansion of $(1 + x)^n$ will be equal,if

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