Alternating series test

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${\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}$
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In mathematical analysis, the alternating series test proves that an alternating series is convergent when its terms decrease monotonically in absolute value and approach zero in the limit. The test was devised by Gottfried Leibniz and is sometimes known as Leibniz's test, Leibniz's rule, or the Leibniz criterion. The test is only sufficient, not necessary, so some convergent alternating series may fail the first part of the test.^[1][2][3]

For a generalization, see Dirichlet's test.^[4][5][6]