convergent sequence
A sequence in which the difference between the nth term and the (n+1)th term decreases as n increases.

For example, {1/3, 1/32, 1/33, 1/34, ...} is a convergent sequence, but {3, 32, 33, 34, ...} is not. A convergent sequence always has a limit. Since the nth term of the above sequence approaches zero as n becomes infinitely large, the limit is 0.

Related Terms: convergent series, divergent sequence

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