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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:

The series converges if the following conditions are met:

  

 

See also

Convergent series, divergent series, limit, alternating series remainder

 

   this page updated 29-jul-08
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons 		Featured in NCTM Web Bytes NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes