Geometric Series Question

Question

0

633

1

+49

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

Yoink Feb 3, 2019

Guest · Answer 1 · 2019-02-03T05:15:00

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