The middle term in the expansion of (1 + x)^{ | vedclass

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(C) For the expansion of $(1 + x)^{2n}$,the total number of terms is $2n + 1$,which is odd.Therefore,there is only one middle term,which is the $\left

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$\frac{(2n)!}{(n!)^2} x^n$

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(C) For the expansion of $(1 + x)^{2n}$,the total number of terms is $2n + 1$,which is odd.Therefore,there is only one middle term,which is the $\left(\frac{2n}{2} + 1\right)$-th term,i.e.,the $(n + 1)$-th term.The general term $T_{r+1}$ in the expansion of $(1 + x)^{2n}$ is given by $T_{r+1} = {}^{2n}C_r x^r$.For $r = n$,the middle term is $T_{n+1} = {}^{2n}C_n x^n$.Using the formula ${}^{2n}C_n = \frac{(2n)!}{n! n!}$,we get the middle term as $\frac{(2n)!}{(n!)^2} x^n$.

The middle term in the expansion of $(1 + x)^{2n}$ is

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