If n is a positive integer,then the coefficie | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) We know that the series expansion of $(1+x)^{-2}$ is given by:$(1+x)^{-2} = 1 - 2x + 3x^2 - 4x^3 + \ldots$Therefore,the given expression can be wr

Vedclass · Accepted Answer

$^{(2n)}C_6$

Vedclass · Answer

(C) We know that the series expansion of $(1+x)^{-2}$ is given by:$(1+x)^{-2} = 1 - 2x + 3x^2 - 4x^3 + \ldots$Therefore,the given expression can be written as:$(1-2x+3x^2-4x^3+\ldots)^{-n} = [(1+x)^{-2}]^{-n} = (1+x)^{2n}$Now,using the Binomial Theorem,the general term in the expansion of $(1+x)^{2n}$ is given by:$T_{r+1} = ^{(2n)}C_r x^r$To find the coefficient of $x^6$,we set $r = 6$:$T_{6+1} = ^{(2n)}C_6 x^6$Thus,the coefficient of $x^6$ is $^{(2n)}C_6$.

If $n$ is a positive integer,then the coefficient of $x^6$ in the expansion of $(1-2x+3x^2-4x^3+\ldots)^{-n}$ is

Similar Questions

Consider the data on $x$ taking the values $2^0, 2^1, 2^2, \ldots, 2^n$ with frequencies ${}^nC_0, {}^nC_1, {}^nC_2, \ldots, {}^nC_n$ respectively. If the mean of this data is $\frac{728}{2^n}$,then $n$ is equal to

The sum of coefficients in the expansion of $(x + 2y + 3z)^8$ is

Prove that $\sum\limits_{r = 0}^n {3^r \,^nC_r} = 4^n$.

If the sum of the coefficients in the expansion of $(\alpha x^2 - 2x + 1)^{35}$ is equal to the sum of the coefficients in the expansion of $(x - \alpha y)^{35}$,then $\alpha = $

The coefficient of $x^6$ in the power series expansion of $\frac{x^4-12x^2+7}{(x^2+1)^3}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module