With n being a positive integer, the series Σ(1/n^p) for n=1 to ∞, for p > 1 is
Options:
(A) convergent
(B) divergent
(C) asymptotic
(D) oscillatory
Official Answer Key:
A
Step-by-Step Solution & Explanation
This is the standard p-series, Σ 1/n^p. By the p-series test, the series converges if and only if p > 1 and diverges for p ≤ 1. Since p > 1 is given, the series is convergent → option (A). Option (B) is the p ≤ 1 case (e.g. harmonic series, p=1); (C) and (D) do not describe the behaviour of a positive monotonically-decreasing term series.
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