If a series is convergent, then will there be a sum as n goes to infinity?

Question

If a series is convergent, then will there be a sum as n goes to infinity?

Answer 1

Yes.  You did say *series*, not sequence, and series means the combination of all of the previous numbers.

If you meant sequence, then the answer is no.

For example:  S = 8 + 1/n.  In this case you would have infinitely many (8 + a small amount)s and that would sum to infinity, even though the *sequence* converges to 8.