In mathematics, the sum of infinitely many numbers, whose relationship can typically be expressed as a formula or a function. An infinite series that results in a finite sum is said to converge (&see; convergence).
One that does not, diverges. Mathematical analysis is largely taken up with studying the conditions under which a given function will result in a convergent infinite series. Such series (e.g., the Fourier series) are particularly useful in solving differential equations.
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