Question

9-36. comparison tests use the comparison test or the limit

comparison test to determine whether the following series converge.
#21.

Answer 1

The comparison test and the limit comparison test are used to determine whether a series converges. The comparison test compares the series to be tested with a comparison series, while the limit comparison test compares the ratio of the terms of the series to be tested with a known convergent series.

Step-by-step explanation:

The comparison test is a method used to determine whether a series converges. There are two versions of the comparison test: the comparison test and the limit comparison test.

1. Comparison Test: If two series have the same signs and the series to be tested is less than or equal to the comparison series, and the comparison series converges, then the series being tested also converges. Similarly, if the comparison series diverges, then the series being tested also diverges.
2. Limit Comparison Test: Compare the series to be tested with a known series that converges. Take the limit of the ratio of the terms of both series. If the limit is a positive, finite number, then both series either converge or diverge. If the limit is 0 or infinity, the series being tested diverges.