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Putnam 2008 A4

Source:

December 8, 2008
Putnamlogarithmsintegrationfloor functionPutnam calculus

Problem Statement

Define f:Rā†’R f: \mathbb{R}\to\mathbb{R} by f(x)\equal{}\begin{cases}x&\text{if }x\le e\\ xf(\ln x)&\text{if }x>e\end{cases} Does \displaystyle\sum_{n\equal{}1}^{\infty}\frac1{f(n)} converge?
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