Power Series

A power series is a way to express a function using an infinite sum of terms, each consisting of a variable raised to a power and multiplied by a coefficient. It looks like this: \( a_0 + a_1x + a_2x^2 + a_3x^3 + \ldots \), where \( a_0, a_1, a_2, \) etc. are constants and \( x \) is a variable. Power series are useful in mathematics and physics because they can represent complex functions, making it easier to analyze and approximate them near a certain point.