**Alternating Series Test**

A convergence test for alternating series.

Consider the following alternating series (where n) and/or its equivalents:\[\sum\limits_{k = 1}^\infty {{{\left( { - 1} \right)}^{k + 1}}{a_k}} = {a_1} - {a_2} + {a_3} - {a_4} + \cdots \] The series converges if the following conditions are met. 1. 2. \(\mathop {\lim }\limits_{n \to \infty } {a_n} = 0\) |

**See also**

Convergent series, divergent series, limit, alternating series remainder

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