Can Leibniz's criterion for alternating series be used to show divergence?
If the test fails, can you conclude that the given series diverges?
2026-03-30 16:05:03.1774886703
Show divergence with Leibniz's criterion for alternating series
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One of the hypotheses of the Leibniz criterion is that the $n$-term of the series goes to zero. If this condition is not satisfied then indeed the series is divergent.
The other condition is that the absolute value of the $n$-th term is a monotone function of $n$. The failure of this condition does not necessarily imply that the series is divergent.