Write the Fourier series representation of the periodic * function f (t) if in one period f(1) A S(1) = { - n

Consider the 27-periodic function f(x) defined on [-, π] by the formula f(x) = cos(). (a) Find the Fourier series expansion of f(x). (b) Use part (a) to find the sum of the following series: A = n=1 (-1) ¹+1 4n² - 1 and B=24²-1

(Hint In part d) using the Fourier series of this problem together with simple algebra, Note that we are shortly going to prove the fact that if ∑|f^(n)|<∞∑|f^(n)|<∞ then the Fourier series of ff converges uniformly to ff. You may use this fact in your solution.)