2-Apr-1995

Unsolved Problem 14:

What is the value of 1/1+1/8+1/27+1/64+1/125+...?

The nth term is the reciprocal of n^3.
If 3 is replaced by 2, it is known that the series sums to (pi^2)/6.
If 3 is replaced by 4, it is known that the series sums to (pi^4)/90.

Reference:

[Dunham 1990]
William Dunham, Journey Through Genius: The Great Theorems of Mathematics. John Wiley and Sons. New York: 1990. Page 222.
A Series involving 1/n^3
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