Convergent Series

Convergent Series

In mathematics, a series is the sum of the terms of a sequence of numbers.

Given a sequence, the nth partial sum is the sum of the first n terms of the sequence, that is,

A series is convergent if the sequence of its partial sums converges. In more formal language, a series converges if there exists a limit such that for any arbitrarily small positive number, there is a large integer such that for all ,

A series that is not convergent is said to be divergent.

Read more about Convergent Series:  Examples of Convergent and Divergent Series, Convergence Tests, Conditional and Absolute Convergence, Uniform Convergence, Cauchy Convergence Criterion

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