Consider the series

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

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.

Related theory

Browse the problem library