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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