series theorem states that if a series converges conditionally, it is possible to rearrange the terms of the series in such a way that the series converges to any value, or even diverges. Uniform convergence Let be a sequence of functions. The series is said to converge uniformly to f if the sequence of partial sums defined by converges uniformly to f. There is an analogue of the comparison test for infinite series of functions called the Weierstrass M-test. Cauchy convergence criterion The Cauchy convergence criterion states that a series converges if and only if the sequence of partial sums is a Cauchy sequence. This means that for every there is a positive integer such that for all we have which is equivalent to See also Normal convergence List of mathematical series External links Weisstein, Eric (2005). Riemann Series Theorem. Retrieved May 16, 2005. Mathematical series Convergence (mathematics)