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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 3, 2019
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S =sumfor(n, 1,∞ , (1/(2*n)^3))=0.1502570505........
T =sumfor(n, 1,∞ , (1/(2*n -1)^3))=1.051799728.......
S/T =0.1502570505 / 1.051799728 =1 /7

 

Which is the same as:

∑[(1/(2*n)^3)), n, 1, ∞] / ∑[(1/(2*n - 1)^3)), n , 1, ∞] = 1/7

 Feb 3, 2019

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