Mathematical property of infinite series, integrals on unbounded regions, and certain sequences of numbers. An infinite series is convergent if the sum of its terms is finite. The series + + + + + ... sums to 1 and thus is convergent. The harmonic series 1 + + + + + ... does not converge. An integral calculated over an interval of infinite width, called an improper integral, describes a region that is unbounded in at least one direction. If such an integral converges, the unbounded region it describes has finite area. A sequence of numbers converges to a particular number when the difference between successive terms becomes arbitrarily small. The sequence 0.9, 0.99, 0.999, etc., converges to 1.
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