Let S = 1/2^3 - 1/4^3 + 1/6^3 - 1/8^3 + ...

and

T = 1/1^3 - 1/3^3 + 1/5^3 - 1/7^3 + ...

Find S/T.

S = [(3 ζ(3))/32]

T = [π^3/32]

S / T = [(3 ζ(3))/32] / [π^3/32]

S / T = (3 ζ(3)) / π^3

ζ(3) - This is called "Riemann zeta function" = 1.202056903159594285...etc.

Note: If you don't understand it, consult your Math Teacher.