How would I define a bounded series?

Question

Please note that I am talking about a series and NOT  a sequence

Answer 1

Consider the sum S_n for n ≥ 1, S_nis bounded above iff ∃ an M | S_n ≤ M.

The same for bounded below withe the modification S_n ≥ M.

If the two exist then the series is just called bounded.