The coefficient of x^-6, in the expansion of ((4 x / 5)+frac52 x^2)^9, is

Coeff of x^-6 in ((4 x / 5)+frac52 x^2)^9 T_r+1 = ^9 C_r((4 x / 5))^9-r(frac52 x^2)^r \ 9-3 r =-6 \ r =5 Coeff of x^-6= ^9 C_5((4 / 5))^4((5 / 2))^5 =5040

The coefficient of x6 in the expansion of frac 4 x5frac... | (Mathematics)

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

$\begin{aligned} T_{r+1} & ={ }^{9} C_{r}\left(\frac{4 x}{5}\right)^{9-r}\left(\frac{5}{2 x^{2}}\right)^{r} \\ 9-3 r & =-6 \\ r & =5 \end{aligned} \\$ Coeff of $x^{-6}={ }^{9} C_{5}\left(\frac{4}{5}\right)^{4}\left(\frac{5}{2}\right)^{5}$ $=5040$

Explanation

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