The middle term in the expansion of {left( x | vedclass

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(B) For the expansion of $(x + a)^n$,if $n$ is even,the middle term is the $(\frac{n}{2} + 1)$-th term.Here,$n = 10$,which is even.Therefore,the middl

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$^{10}C_5$

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(B) For the expansion of $(x + a)^n$,if $n$ is even,the middle term is the $(\frac{n}{2} + 1)$-th term.Here,$n = 10$,which is even.Therefore,the middle term is the $(\frac{10}{2} + 1) = 6$-th term,denoted as $T_6$.The general term $T_{r+1}$ in the expansion of $(x + a)^n$ is given by $T_{r+1} = ^nC_r x^{n-r} a^r$.For $T_6$,we have $r = 5$.Substituting the values,$T_6 = ^{10}C_5 (x)^{10-5} (\frac{1}{x})^5$.$T_6 = ^{10}C_5 x^5 \cdot \frac{1}{x^5} = ^{10}C_5$.Thus,the middle term is $^{10}C_5$.

The middle term in the expansion of ${\left( x + \frac{1}{x} \right)^{10}}$ is

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