Mathematics

Mathematics

Problem

Consider the series ∑n=1∞1nα+n\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^{\alpha}+n}. Which of the following best describes its convergence in terms of the real parameter α\alpha? a) It diverges for every real α\alpha. b) It converges for all α>0\alpha>0. c) It converges if and only if α>1\alpha>1. d) It converges for all α≥1\alpha\ge 1.

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