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A sequence of numbers, xn (where n = 1, 2, 3, ...), is said to converge to a limit L if, given any positive e, however small, it is possible to find an integer k such that |xn - L| < e for all n > k.

In other words, after a certain point (k) all terms of the sequence are closer to the limit (L) than any tiny number.

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Q: What is convergence in numeric math?
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