Editing Power series (section)

===Geometric series, exponential function and sine===
The [[geometric series]] formula
<math display="block">\frac{1}{1 - x} = \sum_{n=0}^\infty x^n = 1 + x + x^2 + x^3 + \cdots,</math>
which is valid for <math display="inline">|x| < 1</math>, is one of the most important examples of a power series, as are the [[exponential function]] formula
<math display="block">e^x = \sum_{n=0}^\infty \frac{x^n}{n!} = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots</math>
and the [[Taylor_series#Trigonometric_functions|sine formula]]
<math display="block">\sin(x) = \sum_{n=0}^\infty \frac{(-1)^n x^{2n+1}}{(2n + 1)!} = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots,</math>
valid for all real ''x''.  These power series are examples of [[Taylor series]] (or, more specifically, of [[Maclaurin series]]).