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Theorem: Maclaurin Series of the Exponential Function

For every real number xx,

ex=∑n=0∞xnn!=1+x+x22!+x33!+⋯ ,e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots,

and the series on the right is the Maclaurin series of exe^x.

25 viewsMathematics · Single Variable Calculus
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