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For a fixed constant $k$ and for a particular value of $n$, but for all $x$, we have

$$ f(x)+f(x+1)+....+f (x+n)=k. $$ How do we find the period of the function?

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    You may want to introduce some constraints, otherwise the constant function $f(x)=\frac{k}{n+1}\,$ has *any* real number as a period. – 2017-02-23

1 Answers 1

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$\sum_\limits{i=0}^n f(x+i) = k$

$\sum_\limits{i=0}^n f(x+1+i) = \sum_\limits{i=0}^n f(x+i) + f(x+n+1) - f(x) = k$

$f(x+n+1) = f(x)$