High Quality Content by WIKIPEDIA articles! The alternating series test is a method used to prove that infinite series of terms converge. If the limit of the sequence an equals 0 as n approaches infinity, and each an is smaller than an-1, then the series converges. It is perfectly possible for a series to have its partial sums Sk fulfill this last condition without the series being alternatingIn the proof of convergence we saw that S2n + 1 is monotonically increasing

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