Mathematics

Mathematics

Problem

When investigating the convergence of the series ∑n=1∞1n3\displaystyle\sum_{n=1}^{\infty}\frac{1}{n^{3}}, which improper integral is directly associated with the terms of the series? a) ∫1∞1x2 dx\displaystyle \int_{1}^{\infty}\frac{1}{x^{2}}\,dx b) ∫011x3 dx\displaystyle \int_{0}^{1}\frac{1}{x^{3}}\,dx c) ∫1∞1x3 dx\displaystyle \int_{1}^{\infty}\frac{1}{x^{3}}\,dx d) ∫1∞1x3/2 dx\displaystyle \int_{1}^{\infty}\frac{1}{x^{3/2}}\,dx

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