How to calculate Madelung's constant for NaCl?
The series $\displaystyle \frac{6}{1}-\frac{12}{\sqrt{2}}+\frac{8}{\sqrt{3}}-\frac{6}{2}+\frac{24}{\sqrt{5}}\pm\ldots$ diverges as has been proven in 1951.

The correct value can be obtained by summation over lattice cubes with edge length $2n+1$ and getting the limit for $n \to \infty$. This has been shown in 1985.

Wikipedia provides more information and further reading on this.