# Power series

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Power series are infinite series of the form Σaₙxⁿ (where n is a positive integer). Even though this family of series has a surprisingly simple behavior, it can be used to approximate very elaborate functions.

## Power series function representation using algebra

Now that we're familiar with the idea of an infinite series, we can now think about functions that are defined using infinite series. In particular, we'll begin to look at the power series representation of a function, which are kind of like infinite polynomials. In later tutorials, we'll use calculus to find expressions of several common functions as power series.

## Taylor series approximations

As we've already seen, Maclaurin series are special cases of Taylor series centered at 0. We'll now focus on more generalized Taylor series.