For the series

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

Problem

For the series ∑n=1∞(−1)n+1np\displaystyle \sum_{n=1}^{\infty}\dfrac{(-1)^{n+1}}{n^{p}}, for which values of pp does the series converge conditionally but not absolutely? (a) p=1p=1 (b) p>1p>1 (c) 0<p≤10<p\le 1 (d) 0<p<10<p<1

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