According to my calculus book two parts to testing an alternating series for convergence. Let s = Ʃ(-1)(adsbygoogle = window.adsbygoogle || []).push({}); ^{n}b_{n}. The first is that b_{n + 1}< b_{n}. The second is that the lim_{n[itex]\rightarrow[/itex]∞}b_{n}= 0. However, isn't the first condition unnecessary since b_{n}must be decreasing if the limit is zero. I can't think of any example where the limit will be zero and the function is increasing (assuming b_{n}is not negative which would not really make sense since the series is alternating).

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# Alternating Series Convergence Test

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