User:Jaume Oliver Lafont/A000796

$\sum_{k=0}^\infty \left(\frac{1}{4k+1}-\frac{1}{4k+3}\right) = \frac{\pi}{4}$

Multiplying both sides by 4,

$\sum_{k=0}^\infty \left(\frac{4}{4k+1}-\frac{4}{4k+3}\right) = \pi$ (1)

$\sum_{k=0}^\infty \left(\frac{1}{4k+1}-\frac{1}{4k+5}\right) = 1$

Multiplying both sides by c,

$\sum_{k=0}^\infty \left(\frac{c}{4k+1}-\frac{c}{4k+5}\right) = c$ (2)

Subtracting equation (2) from equation (1),

$\sum_{k=0}^\infty \left(\frac{4-c}{4k+1}-\frac{4}{4k+3} + \frac{c}{4k+5}\right)= \pi - c$