A) \[\frac{a-b}{r\,!}\]
B) \[\frac{a-br}{r\,!}\]
C) \[{{(-1)}^{r}}\frac{a-br}{r\,!}\]
D) None of these
Correct Answer: C
Solution :
\[(a+bx){{e}^{-x}}\] \[=(a+bx)\left\{ 1-\frac{x}{1\ !}+\frac{{{x}^{2}}}{2\ !}-\frac{{{x}^{3}}}{3\ !}+.......+{{(-1)}^{n}}\frac{{{x}^{n}}}{n\ !}+...... \right\}\] The coefficient of\[{{x}^{r}}\]\[=a\frac{{{(-1)}^{r}}}{r\ !}+b\frac{{{(-1)}^{r-1}}}{(r-1)\ !}=\frac{{{(-1)}^{r}}}{r\ !}(a-br)\].
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