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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.