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,$n = 18$,which is even.Therefore,the mid

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$-^{18}C_9$

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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,$n = 18$,which is even.Therefore,the middle term is the $(\frac{18}{2} + 1)^{th} = 10^{th}$ term.The general term $T_{r+1}$ in the expansion of $(x - \frac{1}{x})^{18}$ is given by $T_{r+1} = ^{18}C_r (x)^{18-r} (- \frac{1}{x})^r$.For the $10^{th}$ term,$r = 9$.$T_{10} = ^{18}C_9 (x)^{18-9} (- \frac{1}{x})^9$$T_{10} = ^{18}C_9 (x)^9 (-1)^9 (\frac{1}{x})^9$$T_{10} = ^{18}C_9 (x)^9 (-1) (\frac{1}{x^9})$$T_{10} = -^{18}C_9$.

The middle term in the expansion of ${\left( {x - \frac{1}{x}} \right)^{18}}$ is

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