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.
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See
also
Limit
comparison test
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