Question

Find the middle terms in the expansion of ${(x^2+\frac{1}{x})}^{11}$

Answer 1

Here power of the expansion, $n=11$

Degree$=n+1=11+1=12$

n is odd so two middle terms will be, i.e $\left(\frac{(n+1)}{2}\right)=6$th term and $\left(\frac{(n+1)}{2}\right)+1)=7$th term

$T_6=(\frac{11}{5})\times {\left(x^2\right)}^6\times {\left(\frac{1}{x}\right)}^5$

$T_7=(\frac{11}{6})\times {\left(x^2\right)}^5\times {\left(\frac{1}{x}\right)}^6$