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Comparison Test

A convergence test which compares the series under consideration to a known series. Essentially, the test determines whether a series is "better" than a "good" series or "worse" than a "bad" series. The "good" or "bad" series is often a p-series.

 

If an , cn , and dn are all positive series, where cn converges and dn diverges, then:

1. If an cn for all n N for some fixed N, then an converges.

2. If an dn for all n N for some fixed N, then an diverges.

 

See also

Limit comparison test

 


  this page updated 21-feb-16
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes