By Definition, a series $\displaystyle \sum_{n=1}^\infty a_n$ converges if it's sequence of partial sums $\displaystyle S_n = \sum_{k=1}^n a_k$ converges.
My question is, is the converse true?
If $\displaystyle \sum_{n=1}^\infty a_n$ converges does it mean $\{S_n\}$ converges?
Best Answer
This community wiki solution is intended to clear the question from the unanswered queue.
We define convergence of a series as follows:
When stating definitions, authors write "if" instead of "if and only if" as mentioned in the comments.