An Alternating Sum
Calculus
Level
5
\[S=\sum_{n=-\infty}^{\infty} \dfrac{(-1)^n}{1+n^2}=\dfrac{a\pi e^{b\pi}}{e^{c\pi}-1},\]
where \(a,b,c \) are natural numbers. Find \(a+b+c\).
Note: Please avoid using wolfram alpha.
Hint: Think about the Fourier transform of \(f(x)=e^{-|ax|}\).
by
Pratik Shastri