MathDB

A4

Part of 2008 Putnam

Problems(1)

Putnam 2008 A4

Source:

12/8/2008
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?
Putnamlogarithmsintegrationfloor functionPutnam calculus