+0  
 
0
39
2
avatar

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.

 Oct 21, 2022
 #1
avatar
0

S/T = 2/5

 Oct 22, 2022
 #2
avatar
0

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

 Oct 22, 2022

26 Online Users

avatar