这里想说的是无限级数是否可以使用结合律,交换律显然不成立。例如Sum(1/n * (-1)^(n+1)) {n = 1 -> inf) 级数是收敛的。
1 - 1/2 + 1/3 - 1/4... = ln2
但 1 + 1/3 + 1/5 + 1/7... 是发散的, -1/2 -1/4-1/6... 也是发散的。
Riemann series theorem if an infinite series of real numbers is conditionally convergent, then its terms can be arranged in a permutation so that the new series converges to an arbitrary real number, or diverges.