The coefficient of `x^(n)` in the expansion of `(a+bx+cx^(2))/(e^(x))` is

Options

A. `(-1)^(n)/(n!){cn^(2)-(b+c)(n+a}`
B. `(-1)^(n)/(n!){cn^(2)+(b+c)(n+a}`
C. `(-1)^(n)/(n!){cn^(2)+(b+c)(n-a}`
D. none of these

Explanation

To find the coefficient of \(x^n\) in the expansion of \(\frac{a + bx + cx^2}{e^x}\), we can follow these steps:

### Step 1: Rewrite the expression
We can rewrite the expression as:
\[ a + bx + cx^2 \cdot e^{-x} \]
This is because \(\frac{1}{e^x} = e^{-x}\).
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