Find the middle terms in the expansions of le | vedclass

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

Question

(A) In the expansion of $(a+b)^{n}$,if $n$ is odd,there are two middle terms,namely the $\left(\frac{n+1}{2}\right)^{th}$ term and the $\left(\frac{n+

Vedclass · Accepted Answer

$-\frac{105}{8} x^{9}$ and $\frac{35}{48} x^{12}$

Vedclass · Answer

(A) In the expansion of $(a+b)^{n}$,if $n$ is odd,there are two middle terms,namely the $\left(\frac{n+1}{2}ight)^{th}$ term and the $\left(\frac{n+1}{2}+1ight)^{th}$ term.For the expansion $\left(3-\frac{x^{3}}{6}ight)^{7}$,$n=7$,so the middle terms are the $\left(\frac{7+1}{2}ight)^{th} = 4^{th}$ term and the $\left(\frac{7+1}{2}+1ight)^{th} = 5^{th}$ term.$T_{4} = T_{3+1} = {}^{7}C_{3} (3)^{7-3} \left(-\frac{x^{3}}{6}ight)^{3} = \frac{7 	imes 6 	imes 5}{3 	imes 2 	imes 1} 	imes 3^{4} 	imes \left(-\frac{x^{9}}{216}ight) = 35 	imes 81 	imes \left(-\frac{x^{9}}{216}ight) = -\frac{105}{8} x^{9}$.$T_{5} = T_{4+1} = {}^{7}C_{4} (3)^{7-4} \left(-\frac{x^{3}}{6}ight)^{4} = {}^{7}C_{3} 	imes 3^{3} 	imes \frac{x^{12}}{1296} = 35 	imes 27 	imes \frac{x^{12}}{1296} = \frac{35}{48} x^{12}$.Thus,the middle terms are $-\frac{105}{8} x^{9}$ and $\frac{35}{48} x^{12}$.

Find the middle terms in the expansions of $\left(3-\frac{x^{3}}{6}\right)^{7}$.

Similar Questions

The sum of the rational terms in the binomial expansion of $(\sqrt{2} + 3^{1/5})^{10}$ is

Prove that the coefficient of $x^{n}$ in the expansion of $(1+x)^{2n}$ is twice the coefficient of $x^{n}$ in the expansion of $(1+x)^{2n-1}$.

The constant term in the expansion of $\left(1+\frac{1}{x}\right)^{20}\left(30 x(1+x)^{29}+(1+x)^{30}\right)$ is

Let $n$ be a positive even integer. If the ratio of the largest coefficient and the $2^{nd}$ largest coefficient in the expansion of $(1+x)^{n}$ is $11:10$, then the number of terms in the expansion of $(1+x)^{n}$ is:

In the expansion of $(1+x)(1-x^2)(1+\frac{3}{x}+\frac{3}{x^2}+\frac{1}{x^3})^5, x \neq 0$,the sum of the coefficient of $x^3$ and $x^{-13}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module