Twin problems from the Monthly and the Stolz-Cesaro Lemma

TL;DR

This paper provides solutions to two mathematical problems from the American Mathematical Monthly using a unified technique and introduces a new problem that encompasses both.

Contribution

It offers a novel unified approach to solving two distinct problems and proposes a new problem that implies both, advancing problem-solving methods in analysis.

Findings

Unified technique effectively solves both problems

New problem generalizes the original problems

Method demonstrates versatility in mathematical problem solving

Abstract

In this note we present solutions to two problems which appeared in the American Mathematical Monthly. Although the problems seem to be of different nature when it comes to the hypothesis we show that they can be proved using essentially the same technique. In the end, we introduce a new problem which actually implies both.