Verify That the First Four Terms of the Fourier Series

Short Answer

Verify that the first four terms of the Fourier series for the half wave Rectification of the sine function
$f(t)=\sin (2 \pi f t) {f=1} \text { below are: } f(t)=\frac{\sin \pi t}{2}+\frac{1}{\pi}\left[1-\frac{2}{3} \cos 4 \pi t+\frac{2}{15} \cos 8 \pi t\right]$