I need to know about converge series.For example how to identify a converge series.Plz explain.
This is not a consult question. You need either to take a course in basic analysis, or read a book or, at least, check google under "infinite series".
Get Spivaks Calculus and work through it.
A convergent series is a series that converges to a finite value. There are several tests to find if a given series is convergent. First, there's the "number of terms" test. If your series has a finite number of terms, it's convergent. Easily done. There's also the "limit" test. If the terms in your series don't tend to zero, it's not convergent.
There are other tests that can help you out here, but I don't feel like enumerating all of them.
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