# 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