Formulation
A series of the form
where sufficiently large an are non-negative, is called an alternating series. If the sequence an approaches 0 as n approaches infinity, and the absolute value of the sequence an is monotonically decreasing (i.e. for each n), then the series converges. If L is the sum of the series,
then the partial sum
approximates L with error
It is perfectly possible for a series to have its partial sums Sk fulfill this last condition without the series being alternating. For a straightforward example, consider:
Read more about this topic: Alternating Series Test
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