Find the middle term of the expansion of lef | vedclass

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(B) The given expression is $ \left(\frac{10}{x}+\frac{x}{10}\right)^{10} $. Here,the power $ n = 10 $,which is an even number. Therefore,the number o

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$ {}^{10}C_{5} $

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(B) The given expression is $ \left(\frac{10}{x}+\frac{x}{10}ight)^{10} $. Here,the power $ n = 10 $,which is an even number. Therefore,the number of terms in the expansion is $ n + 1 = 11 $. The middle term is the $ \left(\frac{n}{2} + 1ight) $-th term,which is $ \left(\frac{10}{2} + 1ight) = 6 $-th term. The general term of the expansion $ (a+b)^n $ is given by $ T_{r+1} = {}^{n}C_{r} a^{n-r} b^{r} $. For the $ 6 $-th term,$ r = 5 $. $ T_{6} = {}^{10}C_{5} \left(\frac{10}{x}ight)^{10-5} \left(\frac{x}{10}ight)^{5} $. $ T_{6} = {}^{10}C_{5} \left(\frac{10}{x}ight)^{5} \left(\frac{x}{10}ight)^{5} $. $ T_{6} = {}^{10}C_{5} 	imes 1 = {}^{10}C_{5} $.

Find the middle term of the expansion of $ \left(\frac{10}{x}+\frac{x}{10}\right)^{10} $.

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