Question

Find the middle terms in the expansion of ${(x^2+\frac{1}{x})}^7$.

Answer 1

General term, $T_{r+1}={}^7{C}_r(x^2{)}^r{\left(\frac{1}{x}\right)}^{7-r}={}^7{C}_r\cdot x^{2r-7+r}$

$={}^7{C}_r.x^{3r-7}$

As total number of terms are $(n+1)=8$

$\Rightarrow$ Middle terms would be $(\frac{n}{2}$ and ${\frac{n}{2}+1)}^{th}$

$\Rightarrow 4^{th}$ and $5^{th}$

$\Rightarrow 4^{th}$ term $r=3\Rightarrow T_4={}^7{C}_3.x^2$

$5^{th}$ term $r=4$ $\Rightarrow T_5={}^7{C}_4{x}^5$.