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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 25, 2022
 #1
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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.

 Oct 25, 2022

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