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.
closed as not a real question by Qiaochu Yuan Aug 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.