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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