For which of the following series will every possible rearrangement of its terms…

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

For which of the following series will every possible rearrangement of its terms converge to the same sum as the original series? (a)

\displaystyle\sum_{n=1}^{\infty}\dfrac{(-1)^{n+1}}{n^{2/3}}

(b)

\displaystyle\sum_{n=1}^{\infty}\dfrac{(-1)^{n+1}}{n^{3}}

(c)

\displaystyle\sum_{n=1}^{\infty}\dfrac{(-1)^{n+1}}{n}

(d)

\displaystyle\sum_{n=1}^{\infty}(-1)^{n+1}\dfrac{n}{n+1}