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 12 + 14 + 18 + 116 + 132 + ... sums to 1 and thus is convergent. The harmonic series 1 + 12 + 13 + 14 + 15 + ... 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.