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 (not ∞ or −∞), but 
A classical example is given by
which converges to 
, but is not absolutely convergent (see Harmonic series).
The simplest examples of conditionally convergent series (including the one above) are the alternating series.
Bernhard Riemann proved that a conditionally convergent series may be rearranged to converge to any sum at all, including ∞ or −∞; see Riemann series theorem.
See also
References
- Walter Rudin, Principles of Mathematical Analysis (McGraw-Hill: New York, 1964).
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