Editing Alternating series (section)

{{Short description|Infinite series whose terms alternate in sign}}
{{More citations needed|date=January 2010}}
{{Calculus |Series}}

In [[mathematics]], an '''alternating series''' is an [[infinite series]] of terms that alternate between positive and negative signs. In [[capital-sigma notation]] this is expressed
<math display="block">\sum_{n=0}^\infty (-1)^n a_n</math> or <math display="block">\sum_{n=0}^\infty (-1)^{n+1} a_n</math>
with {{math|''a<sub>n</sub>'' > 0}} for all&nbsp;{{mvar|n}}.

Like any series, an alternating series is a [[convergent series]] if and only if the sequence of partial sums of the series [[Limit of a sequence|converges to a limit]]. The [[alternating series test]] guarantees that an alternating series is convergent if the terms {{math|''a<sub>n</sub>''}} converge to 0 [[monotonic function|monotonically]], but this condition is not necessary for convergence.