Which set of conditions on a function guarantees that if converges

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

Problem

Which set of conditions on a function ff guarantees that if ∫1∞f(x) dx\displaystyle\int_{1}^{\infty} f(x)\,dx converges, then the series ∑n=1∞f(n)\displaystyle\sum_{n=1}^{\infty} f(n) also converges? (a) ff is continuous, positive, and increasing on [1,∞)[1,\infty) (b) ff is continuous and non-negative on [1,∞)[1,\infty) (c) ff is continuous, positive, and decreasing on [1,∞)[1,\infty) (d) ff is continuous and decreasing on [1,∞)[1,\infty) but may take negative values

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