I was reading this article of wikipedia: Conditional and absolute convergence It says: "An absolutely convergent sequence is one in which the length of the line created by joining together all of the increments to the partial sum is finitely long." Is that a characterization of absolute convergent sequences? (Does all conditional convergent have infinite long path of partial sums)? I'm not sure I understand this. I would like to see an example of a conditionally convergent series (of real numbers, not complex numbers if possible), and how is the length of this path related to the non-absolute convergence of the series. In other words: Is the definition of conditional convergence equivalent to "the length of the path of partial sums diverge"? If true, any proof? Thanks!