For real numbers

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

For real numbers pp, consider the series ∑n=1∞(−1)n−1n−p\displaystyle\sum_{n=1}^{\infty} (-1)^{n-1} n^{-p}. Identify the set of pp for which the series (i) converges absolutely, (ii) converges conditionally but not absolutely, and (iii) diverges.

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