Written by the Fiveable Content Team • Last updated September 2025
Verified for the 2026 exam
Verified for the 2026 exam•Written by the Fiveable Content Team • Last updated September 2025
Definition
The comparison tests are used to determine the convergence or divergence of a series by comparing it to another known series. There are two types of comparison tests: the direct comparison test and the limit comparison test.
This test compares a given series with another known series term by term. If the known series converges and all terms of the given series are less than or equal to the corresponding terms of the known series, then the given series also converges.
This test compares a given series with another known positive series using limits. If the limit of their ratio exists and is finite (non-zero), then both series either converge or diverge together.
Divergence Test: This test states that if the limit of a sequence does not exist or is not zero, then the corresponding infinite series diverges.