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Periodic extension
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The periodic extension will have value at 1 which is half way the value as you approach 1 from the left (which is 13) and as you approach one from the right (which is 1)
That average value is 7.
FSf(1) = 7 is the answer. Can someone check whether I am right or wrong.

Re: Periodic extension
Hey mathsforumhelp.
The value at discontinuities will be the average of the two values and is pointed out here:
Gibbs phenomenon  Wikipedia, the free encyclopedia
They specify this in terms of F(x) = [f(x) + f(x+)]/2 where F(x) is the fourier series representation f(x) = f(1) = 13*1 = 13 and f(x+) = f(1+) = 1 so (13+1)/2 = 14/2 = 7.