The coefficient of x^-6, in the expansion of ((4x)/(5)+52x^2)^9, is Answer: 5040

Question

The coefficient of ${x}^{-6}$, in the

expansion of ${(\frac{4x}{5}+\frac{5}{2{x}^{2}})}^{9}$, is

Answer: 5040

Accepted Answer

Coeff of ${x}^{-6}$ in ${(\frac{4x}{5}+\frac{5}{2{x}^{2}})}^{9}$

$\begin{gathered} {T}_{r+1} ={}^{9}{C}_{r}{(\frac{4x}{5})}^{9-r}{(\frac{5}{2{x}^{2}})}^{r} \ \ 9-3r =-6 \ \ r =5 \end{gathered}$

Coeff of ${x}^{-6}={}^{9}{C}_{5}{(\frac{4}{5})}^{4}{(\frac{5}{2})}^{5}$

$=5040$

Solutions · 1