Write the coefficient of $x^{n}$ in the expansion of $e^{a - b x}$ .

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Solution

$e^{a - b x} = e^{a} \cdot e^{- b x} = e^{a} (1 + \frac{(- b x)}{1!} + \frac{(- b x)^{2}}{2!} + \frac{(- b x)^{3}}{3!} + . . . . . . . . . . . .)$
Hence coefficient of $x^{n}$ is given by $e^{a} \cdot \frac{(- b)^{n}}{n!}$ .

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