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Infinite Seriesmedium
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Let f(x)f(x)f(x) be a continuous, positive, decreasing function on [1,∞)[1, \infty)[1,∞) such that ∫1∞f(x) dx=5\int_1^{\infty} f(x)\,dx = 5∫1∞​f(x)dx=5. What can be said about ∑n=1∞f(n)\sum_{n=1}^{\infty} f(n)∑n=1∞​f(n)?