Which of the following is a required hypothesis for applying the Integral Test to the…

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

Problem

Which of the following is a required hypothesis for applying the Integral Test to the series ∑n=1∞f(n)\displaystyle \sum_{n=1}^{\infty} f(n)? (a) lim⁡x→∞f(x)=0\displaystyle \lim_{x\to\infty} f(x)=0 (b) ∫1∞f(x) dx converges\displaystyle \int_{1}^{\infty} f(x)\,dx \text{ converges} (c) f(x) is positive for x≥1f(x)\text{ is positive for }x\ge 1 (d) f(x) has only finitely many discontinuities on [1,∞)f(x)\text{ has only finitely many discontinuities on }[1,\infty)

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