Comparison Test

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 ∑ a_n , ∑ c_n , and ∑ d_n are all positive series, where ∑ c_n converges and ∑ d_n diverges, then:

1. If a_n ≤ c_n for all n ≥ N for some fixed N, then ∑ a_n converges.

2. If a_n ≥ d_n for all n ≥ N for some fixed N, then ∑ a_n diverges.

See also

Limit comparison test