# convergent sequence ( to +- infinity or some real number) exist a good test for detect it? [closed]

when i refer to a convergent sequence i mind also sequence that goes to +- infinity ( but only one of them) that is, given any A , there is an N such that is n>N then $a_n > A$ etc.

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What is the question? Please make the body of the post self-contained (the subject line is an indication of what the post is about, not part of the post) – Arturo Magidin Aug 7 '11 at 23:20
We can divide the set of sequence in two sets, the set of convergent sequences, and divergent sequence, in the convergent sequence I´ll consider all the "typical convergent sequences" and the sequence that approach to +- infinity, that is, given any A, exist an N such that n>N implies that $a_n >A$ ( or less than A if the sequence goes to -infinity) . I am asking if exist a good test, that can detect if given a sequence can detect if it is convergent ( in any of the two sense of convergence) I have problems with an exercise that says Let $a_n$ a sequence such that exist C>0 such that $$\f – Daniel Aug 7 '11 at 23:42 trying to prove it , im thinking in using Ceraso Stolz , theorem, and proving that afirmation to the limit of$$ a_{n + 1} - a_n  someone has an idea with that? – Daniel Aug 8 '11 at 3:28
@Daniel, please try to follow the local customs of the site. – Mariano Suárez-Alvarez Aug 8 '11 at 4:05

## closed as not a real question by Qiaochu YuanAug 8 '11 at 13:35

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.

There are many tests for deciding whether a given sequence converges. Which test(s) to use for a particular sequence will depend on what you know about that particular sequence. There is no one-size-fits-all test, except insofar as the definition of convergence could be said to be a test in itself.

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