Which of the following infinite series is conditionally convergent?

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

Problem

Which of the following infinite series is conditionally convergent? (a) ∑n=1∞(−1)n+1n2\displaystyle\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n^{2}} (b) ∑n=1∞1n\displaystyle\sum_{n=1}^{\infty}\frac{1}{n} (c) ∑n=1∞(−1)n+1n\displaystyle\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n} (d) ∑n=1∞(−1)n+12 n\displaystyle\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{2^{\,n}}

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