A power series is an infinite series of the form ∑(a_n)(x-c)^n, where a_n represents the coefficients, x is the variable, and c is the center of the series. It is a fundamental tool in calculus and analysis for representing functions as infinite polynomials, particularly useful for approximating functions and solving differential equations.

Power Series

power series

An infinite series is the sum of an infinite sequence of terms, which can converge to a finite limit or diverge to infinity. Understanding the behavior of infinite series is fundamental in calculus and analysis, as it helps in approximating functions and solving differential equations.

infinite series

Coefficients are numerical or constant multipliers of variables in mathematical expressions, equations, or models that quantify relationships or changes. They are essential in fields like algebra, statistics, and calculus for interpreting the strength and direction of these relationships.

coefficients

the variable

the center of the series

fundamental tool in calculus

analysis for representing functions

infinite polynomials

approximating functions

solving differential equations

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