Question

A series converges then the partial sum sequence is bounded

Answer 1

Theorem 237 (Boundedness) Every convergent sequence is bounded. It is easy to see that the converse of this theorem is not true. We saw in a previous example the sequence{1+(−1)n}, which is bounded but diverges. Theorem 238 (Uniqueness) If a sequence {sn} converges, then its limit is unique.