Conditional convergence
In mathematics, a series or integral is said to be conditionally convergent if it converges, but it does not converge absolutely.Definition
More precisely, a series is said to converge conditionally if
exists and is a finite number, but
A classic example is the alternating series given by which converges to , but is not absolutely convergent.
Bernhard Riemann proved that a conditionally convergent series may be rearranged to converge to any value at all, including ∞ or −∞; see Riemann series theorem. The Lévy–Steinitz theorem identifies the set of values to which a series of terms in Rn can converge.
A typical conditionally convergent integral is that on the non-negative real axis of .
