Mathegoras

Functions › Even, odd and periodic functions › Odd and even functions

Sum of values of a shifted odd function

High school · ●●●○○ 50 pts

Given that f(x)f(x) is an odd function defined on R\mathbb{R} and f(1)=1f(1) = 1. If the graph of f(x)f(x) is translated one unit to the right, the resulting graph is that of an even function. Find the sum f(1)+f(2)+f(3)+…+f(2009)f(1) + f(2) + f(3) + \ldots + f(2009).

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even and odd functionsperiodic functionsfunction transformationsfunctional equations