If the coefficients of the (2r + 1)^{th} term | vedclass

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

Question

(A) The general term $T_{k+1}$ in the expansion of $(1 + x)^n$ is given by $\binom{n}{k} x^k$.The coefficient of the $(2r + 1)^{th}$ term is $\binom{4

Vedclass · Accepted Answer

$14$

Vedclass · Answer

(A) The general term $T_{k+1}$ in the expansion of $(1 + x)^n$ is given by $\binom{n}{k} x^k$.The coefficient of the $(2r + 1)^{th}$ term is $\binom{43}{2r}$.The coefficient of the $(r + 2)^{th}$ term is $\binom{43}{r+1}$.Given that these coefficients are equal,we have $\binom{43}{2r} = \binom{43}{r+1}$.Using the property $\binom{n}{a} = \binom{n}{b}$,we know that either $a = b$ or $a + b = n$.Case $1$: $2r = r + 1 \implies r = 1$.Case $2$: $2r + (r + 1) = 43 \implies 3r + 1 = 43 \implies 3r = 42 \implies r = 14$.Comparing with the given options,the value of $r$ is $14$.

If the coefficients of the $(2r + 1)^{th}$ term and the $(r + 2)^{th}$ term are equal in the expansion of $(1 + x)^{43}$,then the value of $r$ is:

Similar Questions

Find the coefficient of $x^{64}$ in the expansion of $P(x) = (x - 1)^2(x - 2)^3(x - 3)^4 \dots (x - 10)^{11}$.

If the coefficients of $r$-th and $(r+1)$-th terms in the expansion of $(3+7x)^{29}$ are equal,then $r$ is equal to

If the middle term in the expansion of ${\left( {x^2 + \frac{1}{x}} \right)^n}$ is $924x^6$,then $n = $

The numerically greatest term in the expansion of $(2x - 3y)^{13}$ when $x = \frac{7}{2}$ and $y = \frac{3}{7}$ is:

The second,third and fourth terms in the binomial expansion $(x+a)^n$ are $240, 720$ and $1080$ respectively. Find $x, a$ and $n$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module