Power series facts for kids
In mathematics, a power series (in one variable) is an infinite series of the form
where a_{n} represents the coefficient of the nth term, c is a constant, and x varies around c (for this reason one sometimes speaks of the series as being centered at c). This series usually appears as the Taylor series of some known function; the Taylor series article contains many examples.
In many situations c is equal to zero, for example when considering a Maclaurin series. In those cases, the power series takes the simpler form
These power series appear primarily in analysis, but also appear in combinatorics (under the name of generating functions) and in electrical engineering (under the name of the Ztransform). The familiar decimal notation for integers can also be viewed as an example of a power series, but with the argument x fixed at 10. In number theory, the concept of padic numbers is also closely related to that of a power series.
Images for kids

The exponential function (in blue), and the sum of the first n + 1 terms of its Maclaurin power series (in red).