Write the middle term in the expansion of (x+1 x )^ 10 . - Vidyadip

Question

Write the middle term in the expansion of $\Big(\text{x}+\frac{1}{\text{x}}\Big)^{10}.$

✓

Answer

$\Big(\text{x}+\frac{1}{\text{x}}\Big)^{10}$
Hence n = 10, which is even number.
So, $\Big(\frac{10}{2}+1\big)\text{th}$ term i.e., 6th term is the middle term.
$\text{T}_{6}=\text{T}_{5+1}={^\text{10}}\text{C}_{\text{5}}(\text{x})^{10-5}\Big(\frac{1}{5}\Big)^{5}$
$={^\text{10}}\text{C}_{\text{5}}$

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