MathDB
f(na) goes to 0 for all a - Paenza 2010

Source:

August 26, 2010
functionlimitsearchtopologyreal analysis

Problem Statement

Let f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} be a continuous function with the following property: for all α∈R>0\alpha \in \mathbb{R}_{>0}, the sequence (an)n∈N(a_n)_{n \in \mathbb{N}} defined as an=f(nα)a_n = f(n\alpha) satisfies lim⁡n→∞an=0\lim_{n \to \infty} a_n = 0. Is it necessarily true that lim⁡x→+∞f(x)=0\lim_{x \to +\infty} f(x) = 0?
Back to ProblemsView on AoPS