olymmath

Putnam 2008 A4

  • Session A

Define f:R→Rf: \mathbb{R} \to \mathbb{R} by f(x)={xif x≤exf(ln⁡x)if x>e.f(x) = \begin{cases} x & \text{if $x \leq e$} \\ x f(\ln x) & \text{if $x > e$.} \end{cases} Does ∑n=1∞1f(n)\sum_{n=1}^\infty \frac{1}{f(n)} converge?

Curated text Kedlaya Putnam archive. Quoted with source.

Solutions

Human solution Solution 1 by Kiran Kedlaya and Lenny Ng

The terms of the source let olymmath link to this solution but not copy it. Read the solution (Kedlaya Putnam archive).

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