Alternating series

An alternating series is a special kind of series of the form

\infty \sum 𝑛 = 1 (- 1) 𝑛 - 1 𝑎 𝑛

where $𝑎 𝑛 > 0$ for all $𝑛 \in ℕ$ . Such series exhibit a number of special properties, for example, if $𝑎 𝑛$ is non-increasing, the Test for divergence by sequence limit is made stronger giving the Alternating series test. In cases where the alternating series test holds but the series $\sum \infty 𝑛 = 1 𝑎 𝑛$ is divergent, the alternating series is said to be conditionally convergent.

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