# Please show all of your work !!!! We shall find a Fourier series for the function f(x) = x on the interval x \in (?2, 2) extended to a periodic function:

We shall find a Fourier series for the function f(x) = x on the interval x  (?2, 2) extended to a periodic function:

f(x) =  (1)

One application, perhaps unexpected, of such a Fourier series is the evaluation of infinite sums, for instance

S =  (2)

resembling another conditionally-convergent series in the context of the binding energy of crystalline salt. Evaluate (2) by substituting a particular value for x in (1). (We

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