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Putnam 2010 A6


Let f : [0,\infty) \to \Bbb{R} be a strictly decreasing continuous function such that \displaystyle \lim_{x \to \infty}f(x)=0. Prove that \displaystyle \int_0^\infty \frac{f(x)-f(x+1)}{f(x)}dx diverges.

Putnam 2010 A6

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