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avatar+1093 

Let \[S = \frac{1}{2^3} + \frac{1}{4^3} + \frac{1}{6^3} + \dotsb\]and \[T = \frac{1}{1^3} + \frac{1}{3^3} + \frac{1}{5^3} + \dotsb.\]Find $S/T$.

 Feb 15, 2020
 #1
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0

S = Sum[1/n^3; n = 0; n = n + 2; n <= inf] = 1/4*zeta(5) and T = Sum[1/n^3: n = 1; n = n + 2; n <= inf] = 3/4*zeta(5), so S/T = 1/3.

 Feb 15, 2020
 #3
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+1

S = 0.15025711289495
T=1.051799790264645
S/T =0.15025711289495 / 1.051799790264645
S/T = 1 / 7

 Feb 15, 2020
 #4
avatar+110175 
-1

Why don't you put your Latex into the Latex box so that people can read it  ?

 Feb 15, 2020

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