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Source: Romania 1996

August 29, 2005
functionreal analysisreal analysis unsolved

Problem Statement

Suppose that f1,f2,...,fn:R→Rf_1,f_2,...,f_n: \mathbb{R}\rightarrow \mathbb{R} are the periodic functions and f=f1+f2+...+fn,f:R→Rf=f_1+f_2+...+f_n , f:\mathbb{R} \rightarrow \mathbb{R} has an finite limit in +∞+\infty. Prove that ff is the constant function.
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