Coefficient of $x^{10}$ in the expansion of $(2+3 x) e^{-x}$ is

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Aicharya · Accepted Answer

$ \begin{aligned} (2+3 x) e^{-x} & \ & =(2+3 x)\left(1-\frac{x}{1 !}+\frac{x^2}{2 !}-\frac{x^3}{3 !}+\ldotsight) \end{aligned} $ $	herefore$ Coefficient of $x^{10}$ in the above series $ \begin{aligned} & =\frac{2}{10 !}-\frac{3}{9 !} \ & =\frac{1}{10 !}(2-30)=\frac{-28}{10 !} \end{aligned} $

Coefficient of $x^{10}$ in the expansion of $(2+3 x) e^{-x}$ is

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