A power series is a mathematical expression that represents a function as an infinite sum of terms. Each term is composed of a constant coefficient multiplied by a variable raised to a non-negative integer power. The general form of a power series centered at a point c is given by \sum_n=0^\infty a_n (x - c)^n , where a_n are the coefficients and x is the variable. Power series are useful in various fields, including calculus and physics, as they can approximate functions near a specific point. They converge within a certain radius, known as the radius of convergence, which determines the values of x for which the series converges to a finite value.