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/T = 2/5
S = sum_(n=1)^∞ (-1)^(1 + n)/(8 n^3) = (3 ζ(3))/32≈0.112692834671212
T = sum_(n=1)^∞ (-1)^(1 + n)/(-1 + 2 n)^3 = π^3/32≈0.968946146259369
S / T = 0.112692834671212 / 0.968946146259369
==0.11630453880875
