prove-r-1-x-r-1-2-pi-tan-x-r-1-x-r-r-1-x-r-pi-2-4-r-odd-r-even-

Question Number 166168 by alcohol last updated on 14/Feb/22

p r o v e

\underset{r = - \infty}{\sum^{\infty}} \frac{1}{x + (r + \frac{1}{2}) π} = t a n (x)

(\underset{r = - \infty}{\sum^{\infty}} \frac{1}{x + r}) (\underset{r = - \infty}{\sum^{\infty}} \frac{1}{x + r}) = - \frac{π^{2}}{4}

(r = o d d) (r = e v e n)