
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, 1/3^{2}, 1/3^{3}, 1/3^{4}, ...} is a convergent sequence, but {3, 3^{2}, 3^{3}, 3^{4}, ...} 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.

