# How do you find the Maclaurin series of #f(x)=e^(-2x)# ?

I apologize for the poor formatting; I was unable to fit all the terms on one line.

These terms are identical to those in the previously written Maclaurin series.

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To find the Maclaurin series of ( f(x) = e^{-2x} ), we use the general formula for the Maclaurin series expansion of ( e^x ):

[ e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} ]

Substituting (-2x) for (x) in the formula:

[ e^{-2x} = \sum_{n=0}^{\infty} \frac{(-2x)^n}{n!} ]

Simplifying:

[ e^{-2x} = \sum_{n=0}^{\infty} \frac{(-1)^n 2^n x^n}{n!} ]

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