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 pseries.
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
