# Infinite Series

Mathematicians have often run into functions that are too complicated for them to solve or otherwise deal with, and approximations have always been an important component in doing math. For mathematicians trying to take derivatives and integrals algebraically, many expressions have no nice neat solutions, derivatives, integrals, and so on. In general, no differential equations that scientists come across in real life have algebraic solutions, so they have to use other methods. More on differential equations later, but there's an important family of approximations that use *easy* functions to approximate *hard* ones.

## Polynomial Functions

It's easy to solve, differentiate, and integrate polynomial equations—ones such as *y = x*2 and even the following equation:

The terms are all added (or subtracted) one after the other, and there are no trigonometric, logarithmic, or exponential functions involved...