When investigating the convergence of the series

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

Problem

\displaystyle\sum_{n=1}^{\infty}\frac{1}{n^{3}}

, which improper integral is directly associated with the terms of the series? (a)

\displaystyle \int_{1}^{\infty}\frac{1}{x^{2}}\,dx

(b)

\displaystyle \int_{0}^{1}\frac{1}{x^{3}}\,dx

(c)

\displaystyle \int_{1}^{\infty}\frac{1}{x^{3}}\,dx

(d)

\displaystyle \int_{1}^{\infty}\frac{1}{x^{3/2}}\,dx