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

$\begin{array}{1 1} \large\frac{(2n)!}{n!}.x^n \\ \large\frac{(2n)!}{n!.(n-1)!}.x^{n+1} \\ \large\frac{(2n)!}{n!^2}.x^n \\ \large\frac{(2n)!}{(n+1)!.(n-1)!}.x^n \end{array}$

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  • General term in the expansion of $(1+x)^n$ is $T_{r+1}=^nC_rx^r$
The no. of terms in the expansion of $(1+x)^{2n}$ is $2n+1$.
The middle term is $\bigg(\large\frac{2n}{2}$$+1\bigg)^{th}$ term.
$i.e.,$ $(n+1)^{th}$ term is the middle term.
$\therefore T_{r+1}=^{2n}C_n.x^n$
$=\large\frac{(2n)!}{n!.n!}.x^n$ =$=\large\frac{(2n)!}{n!^2}.x^n$
answered Sep 19, 2013 by rvidyagovindarajan_1

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