A series is an infinite addition of an ordered set of terms. The infinite series often contain an infinite number of terms and its nth term represents the nth term of a sequence. A series contain terms whose order matters a lot. If the terms of a rather conditionally convergent series are suitably arranged, the series may be made to converge to any desirable value or even to diverge according to the Riemann series theorem. Let the terms in a series be denoted by the symbol, an , and the nth partial summation be denoted using the following sigma notation for any natural number n:
