Thread: Alternating series convergence?

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?

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.