The coefficient of $x^{-6}$, in the
expansion of $\left(\frac{4 x}{5}+\frac{5}{2 x^{2}}\right)^{9}$, is
Answer (integer)
5040
Solution
Coeff of $x^{-6}$ in $\left(\frac{4 x}{5}+\frac{5}{2 x^{2}}\right)^{9}$
<br/><br/>$$
\begin{aligned}
T_{r+1} & ={ }^{9} C_{r}\left(\frac{4 x}{5}\right)^{9-r}\left(\frac{5}{2 x^{2}}\right)^{r} \\\\
9-3 r & =-6 \\\\
r & =5
\end{aligned}
$$
<br/><br/>Coeff of $x^{-6}={ }^{9} C_{5}\left(\frac{4}{5}\right)^{4}\left(\frac{5}{2}\right)^{5}$
$=5040$
About this question
Subject: Mathematics · Chapter: Binomial Theorem · Topic: Binomial Expansion
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