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In mathematics, the limit comparison test (LCT) (in contrast with the related direct comparison test) is a method of testing for the convergence of an infinite series. Statement [ edit ]
A commonly-used corollary of the integral test is the p-series test. ... This can be proved by taking the logarithm of the product and using limit comparison test. [9 ...
Second is the general limit comparison test: [53] ... The alternating series test can be viewed as a special case of the more general Dirichlet's test: [67] ...
In mathematics, the comparison test, sometimes called the direct comparison test to distinguish it from similar related tests (especially the limit comparison test), provides a way of deducing whether an infinite series or an improper integral converges or diverges by comparing the series or integral to one whose convergence properties are known.
The ratio test and the root test are both based on comparison with a geometric series, and as such they work in similar situations. In fact, if the ratio test works (meaning that the limit exists and is not equal to 1) then so does the root test; the converse, however, is not true.
Comparison test can mean: Limit comparison test , a method of testing for the convergence of an infinite series. Direct comparison test , a way of deducing the convergence or divergence of an infinite series or an improper integral.
The more general class of p-series, =, exemplifies the possible results of the test: If p ≤ 0, then the nth-term test identifies the series as divergent. If 0 < p ≤ 1, then the nth-term test is inconclusive, but the series is divergent by the integral test for convergence.
In mathematics, convergence tests are methods to determine if an infinite series converges or diverges. Pages in category "Convergence tests" The following 17 pages are in this category, out of 17 total.