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A power series is an infinite series of the form ∑(aₙ*xⁿ), where aₙ represents the coefficients of the series, x is a variable, and n ranges from 0 to infinity. These series are used in mathematics to represent functions as an infinite sum of terms, often in the context of calculus and analysis. The convergence of a power series is determined by its radius of convergence, which dictates the values of x for which the series converges. Power series are a fundamental tool in mathematical analysis and have applications in various areas of mathematics and physics.