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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 (seeconvergence). 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.
This entry comes from Encyclopædia Britannica Concise. For the full entry on infinite series, visit Britannica.com.
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