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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 ]
Calculus ′ = () ... If r = 1, the root test is inconclusive, ... This can be proved by taking the logarithm of the product and using limit comparison test. [9] See also
The root test states that: if C < 1 then the series converges absolutely, if C > 1 then the series diverges, if C = 1 and the limit approaches strictly from above then the series diverges, otherwise the test is inconclusive (the series may diverge, converge absolutely or converge conditionally).
Summand limit (term test) Ratio; ... of infinite sequences and infinite series to a well-defined limit. [1] ... calculus is developed using limits rather than ...
In mathematics, the nth-term test for divergence [1] is a simple test for the divergence of an infinite series: If lim n → ∞ a n ≠ 0 {\displaystyle \lim _{n\to \infty }a_{n}\neq 0} or if the limit does not exist, then ∑ n = 1 ∞ a n {\displaystyle \sum _{n=1}^{\infty }a_{n}} diverges.
The ratio test states that: if L < 1 then the series converges absolutely;; if L > 1 then the series diverges;; if L = 1 or the limit fails to exist, then the test is inconclusive, because there exist both convergent and divergent series that satisfy this case.
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