---
type: "problem"
title: "Limit of a sum of periodic functions"
slug: "limit-of-a-sum-of-periodic-functions"
author: "ancient-tree"
tags: ["limit", "periodic functions"]
difficulty: 60
qualityStatus: "unreviewed"
listed: true
origin: "Unknown"
originChapter: ""
originPage: ""
originNote: ""
license: "CC BY-SA 4.0"
---

Let $f$ and $g$ be two periodic functions of respective periods $T_1$ and $T_2$. We also assume that $f(x)+g(x)$ admits a limit as $x$ goes to $+\infty$.

Show that $f+g$ is constant.