Explain briefly why

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Explain briefly why, for a positive decreasing function ff, the value of ∫1∞f(x) dx\displaystyle\int_{1}^{\infty} f(x)\,dx must be less than or equal to ∑n=1∞f(n)\displaystyle\sum_{n=1}^{\infty} f(n).

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