Question

Find the coefficient of $x$ in ${(x^2+\frac{1}{x})}^5$

Answer 1

$T_{r+1}{=}^5{C}_r(x^2{)}^{5-r}{\left(\right(\frac{1}{x}\left)\right)}^r{=}^5{C}_r{x}^{(10-2r-r)}weneed{x}^{1}onlyhence10-3r=1or9=3r\therefore r=3soco-efficeint{=}^5{C}_3=(\frac{5!}{(5-3)!3!})=10$