Keyword Analysis & Research: alternating series test


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How does the alternating series test work?

Alternating series test. The theorem known as "Leibniz Test" or the alternating series test tells us that an alternating series will converge if the terms an converge to 0 monotonically. Proof: Suppose the sequence a n {\displaystyle a_{n}} converges to zero and is monotone decreasing.

Can the alternating series test prove divergence?

The alternating series test is a test for convergence. But if the test fails to show convergence, that doesn't imply divergence. It might be convergent anyway and the alternating series test just isn't adequate to show it. All you can say is that the alternating series test failed to show convergence.


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