(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 interval in which $x$ must lie so that the greatest term in the expansion of $(1 + x)^{2n}$ has the greatest coefficient,is

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The sum of all rational terms in the expansion of $(2^{\frac{1}{5}} + 5^{\frac{1}{3}})^{15}$ is equal to :

DifficultJEE MAIN 2024

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In the expansion of $(1 + 3x + 2x^2)^6$,the coefficient of $x^{11}$ is

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In the expansion of $(1+x)^n$,the coefficients of the $p^{th}$ and $(p+1)^{th}$ terms are respectively $p$ and $q$. Then $p+q$ is equal to:

MediumTS EAMCET 2002

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The coefficient of $x^5$ in the expansion of $(x + 3)^6$ 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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The interval in which $x$ must lie so that the greatest term in the expansion of $(1 + x)^{2n}$ has the greatest coefficient,is

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