Consider the series

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

Problem

Consider the series ∑n=1∞(−1)n 5n3/2\displaystyle \sum_{n=1}^{\infty}\dfrac{(-1)^{n}\,5}{n^{3/2}}. Which statement best describes its convergence? (a) It converges conditionally because the corresponding positive-term series diverges. (b) It diverges because the exponent satisfies p<1p<1. (c) It converges absolutely because the corresponding positive-term series has p>1p>1. (d) It diverges because ∫1∞5x3/2 dx\displaystyle\int_{1}^{\infty}\frac{5}{x^{3/2}}\,dx diverges by the Integral Test.

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