A function f(x) is periodic of period 2 and is defined by Sketch a graph of f(x)

Question:

A function f(x) is periodic of period 2 and is defined by

f(x) = [-2x (- < x 0) 2x (0 < x )

Sketch a graph of f(x) from –2π to 3π and prove that

f(x) =  - 8 -   n=0 1 (2n + 1)  cos (2n + 1)x

Hence show that

=1+  n=1 1 (2n + 1)

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