olymmath

Putnam 2010 A6

  • Session A

Let f:[0,∞)→Rf:[0,\infty)\to \mathbb{R} be a strictly decreasing continuous function such that lim⁡x→∞f(x)=0\lim_{x\to\infty} f(x) = 0. Prove that ∫0∞f(x)−f(x+1)f(x)dx\int_0^\infty \frac{f(x)-f(x+1)}{f(x)} dx diverges.

Curated text Kedlaya Putnam archive. Quoted with source.

Solutions

Human solution Solution 1 by Kiran Kedlaya and Lenny Ng

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