Question

Find the $4^{th}$ term from the end in the expansion of ${[\frac{x^3}{2}-\frac{2}{x^2}]}^9$.

Answer 1

$4^{th}$ term from the end ${(\frac{x^3}{2}-\frac{2}{x^2})}^9$

Now, $4^{th}$ term from the end will be $(9-4+2)$

i.e $7^{th}$ from begining

$T_7=T_{6+1}{\Rightarrow }^9{C}_6{\left(\frac{x^3}{2}\right)}^{9-6}.{\left(\frac{-2}{x^2}\right)}^6$

$\Rightarrow \frac{9\times 3\times 7\times 6!}{6!3!}.\left(\frac{x^9}{3}\right)\left(\frac{64}{x^{12}}\right)$

$\Rightarrow 448x^{-3}$