The Maclaurin series is given as

To get the Maclaurin series for e^{x} we need to find an
expression for the n^{th} derivative of e^{x} at the
origin. This is pretty straight forward since

and each consecutive derivative will just give the same expression, i.e.,

Substituting the above expression in the general series expansion, we derive

to give as the Maclaurin series for the exponential function

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