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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“There is in every either-or a certain naivete which may well befit the evaluator, but ill- becomes the thinker, for whom opposites dissolve in series of transitions.”
—Robert Musil (1880–1942)