What are the values of the seriest 0 and t -pi2and the

Question

Set f (t) = [1 - H (t)] cos t for t ∈ [-Π, 0) ∪ (0, Π), f (0) and f(t + 2Π) = f (t)

a.  Is f(t) even odd or neither,

b. Show that Fourier series of f(t) is

½ cos t - _k=1Σ^∞(4k sin 2kt)) / Π(4k² -1).

c. What are the values of the series t =0 and t = -Π/2 and the corresponding values for original function f(t)? Quote theorems to explain possible discrepancy.

d. Using the Fourier series by taking a proper value for t in this Fourier series, compute the sum of the following infinite series.

_t=1Σ^∞(4(2l - 1) (-1)^l) / Π(4(2l - 1)² -1).