- #1
de1irious
- 20
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How would I show that the series whose terms are given by
(cos n)/(1+n) does not converge absolutely? Thanks so much!
(cos n)/(1+n) does not converge absolutely? Thanks so much!
de1irious said:How would I show that the series whose terms are given by
(cos n)/(1+n) does not converge absolutely? Thanks so much!
de1irious said:You mean this limit comparison test? http://mathworld.wolfram.com/LimitComparisonTest.html
But what limit does it tend to? I thought |cos n| didn't tend to a limit as n--> infinity.
A basic convergence question refers to a problem or scenario in which a series or sequence of numbers is being studied to determine whether it converges or diverges. This is an important concept in mathematics and is commonly encountered in various scientific fields.
Convergence is determined by looking at the behavior of a series or sequence as the number of terms or iterations increases. If the terms or values of the series approach a specific number or value, then the series is said to converge. If the terms become increasingly larger or smaller without approaching a specific value, then the series is said to diverge.
Absolute convergence refers to a series in which the absolute values of the terms converge, while conditional convergence refers to a series in which the terms themselves converge. In other words, absolute convergence is a stricter condition than conditional convergence.
No, a series can only converge to one value. The behavior of a series as the number of terms increases should be consistent and approach a specific value. If a series converges to multiple values, it is considered to be divergent.
Convergence is important in science because it allows us to make predictions and analyze data. Many real-world phenomena can be modeled using series or sequences, and determining their convergence can help us understand and make predictions about these phenomena. It is also a fundamental concept in many scientific fields, including physics, engineering, and economics.