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Alternating Series Remainder

A quantity that measures how accurately the nth partial sum of an alternating series estimates the sum of the series.

Consider the following alternating series (where an > 0 for all n) and/or its equivalents.

If the series converges to S by the alternating series test, then the remainder

can be estimated as follows for all n ≥ N:

Here, N is the point at which the values of an become non-increasing:

 

See also

Remainder of a series, convergence tests, divergent series

 

   this page updated 2-apr-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