- #1
Saitama
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Homework Statement
Let ## n \geq 2## be a fixed integer. ##f(x)## be a bounded function defined in ##f:(0,a) \rightarrow R## satisfying
[tex]f(x)=\frac{1}{n^2}\sum_{r=0}^{(n-1)a} f\left(\frac{x+r}{n}\right)[/tex]
then ##f(x)## =
a)-f(x)
b)2f(x)
c)f(2x)
d)nf(x)
Homework Equations
The Attempt at a Solution
I see no way of simplifying the summation. I need a few hints to start with.
Any help is appreciated. Thanks!