Why is sigma (-1)^n/n a convergent series while sigma 1/n is a divergent p-series?
...is it because half the terms are used for either sign +/- and therefore each set decays more rapidly than 1/n?
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Let then obviously On the other hand, is a strictly decreasing sequence for Hence, by Leibniz test the series converges.
But, this series converges conditionally, since and diverges.
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