Under what conditions does an alternating series converge? an alternating series ∞ an n = 1 = ∞ (−1)n − 1bn, n = 1 where bn = |an|, converges if 0 < bn + 1 ≤ bn for all n.

First, write the alternate series as where the term is positive. From the Cauchy criterion we already know that . So, in order to  assure the convergence we only need to ask that the term   is monotonically decreasing.

Step-by-step explanation:

This is the Leibniz criterion for the convergence of alternate series.

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step-by-step explanation: