MathDB
Putnam 1964 B1

Source: Putnam 1964

March 5, 2022
PutnamConvergence

Problem Statement

Let uku_k be a sequence of integers, and let VnV_n be the number of those which are less than or equal to nn. Show that if ∑k=1∞1uk<∞,\sum_{k=1}^{\infty} \frac{1}{u_k } < \infty, then lim⁡n→∞Vnn=0.\lim_{n \to \infty} \frac{ V_{n}}{n}=0.
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