This is the sequence that can be used to find an exact value of pi
4/1−4/3+4/5−4/7+4/9−4/11…..(to infinity) =
Or (1/1−1/3+1/5−1/7+1/9−1/11….. (to infinity) )= /4
Given that we have this result, is it possible to find the value of the sequence 1-3+5-7+9-11….. ?
If you are interested in the “normalized” value of $\beta(-1)$, use $\beta(-k)=\dfrac{E_k}2$, where $E_k$ is the $k^{th}$ Euler number.