8.4: Alternating Series - Mathematics LibreTexts
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WEBSep 29, 2023 · Alternating Series Estimation Theorem If the alternating series \(\sum_{k=1}^{\infty} (-1)^{k+1}a_k\) has positive terms \(a_k\) that decrease to zero as \(k \to \infty\text{,}\) and \(S_n = \sum_{k=1}^{n} (-1)^{k+1}a_k\) is the \(n\)th partial sum of the alternating series, then
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