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

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

A

10⥂C41x10 ⥂ C_{4}\frac{1}{x}

B

10⥂C510 ⥂ C_{5}

C

10⥂C5x10 ⥂ C_{5}x

D

10⥂C7x410 ⥂ C_{7}x^{4}

Answer

10⥂C510 ⥂ C_{5}

Explanation

Solution

∵ n is even so middle term T(102+1)=T6T_{\left( \frac{10}{2} + 1 \right)} = T_{6}

⇒ T6=T5+1=10⥂C5x5.1x5=10⥂C5T_{6} = T_{5 + 1} =^{10} ⥂ C_{5}x^{5}.\frac{1}{x^{5}} =^{10} ⥂ C_{5}