if f(x) = 1/2(pi-x), find the fourier series of period 2pi in the interval (0,2pi). Hence, deduce that 1-1/2+1/5-1/7+...=pi/4

Question

if f(x) = \(f(x) = \frac{1}{2}(\pi-x)\), find the fourier series of period 2\(\pi\) in the interval (0,\(2\pi\)). Hence, deduce that \(1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+...=\frac{\pi}{4}\)