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  4. The term independent of x in the expansion of (x- (3 /x2))18

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Q. The term independent of $x$ in the expansion of $(x- \frac {3} {x^2})^{18}$

Binomial Theorem

Solution:

$T_{r+1} = \,{}^{18}c_{r}x^{18-r} \left(-\frac{3}{x^{2}}\right)^{r}$
$= \,{}^{18}c_{r}x^{18-r-2r}\left(-3\right)^{r}$
$\therefore 18 - 3r = 0$
$\Rightarrow r = 6$
$\therefore $ reqd. term $=\,{}^{18}c_{6}\left(-3\right)^{6} = \,{}^{18}c_{6}\left(3\right)^{6}$.