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Alternating Series Test

A convergence test for alternating series.

Consider the following alternating series (where an > 0 for all 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. anan +1 for all nN, where N ≥ 1, and

2. \(\mathop {\lim }\limits_{n \to \infty } {a_n} = 0\)

 

See also

Convergent series, divergent series, limit, alternating series remainder

 


  this page updated 19-jul-17
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
Copyright © 2000 by Bruce Simmons
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