How to calculate Madelung's constant for NaCl? Madelung's constant for $\ce{NaCl}$ is $1.748$. 
What I tried to so is sum up all the individual interactions into $1$ component where the $X$s are the nucleus and the electron if it was a $2$ atom system. Is this the correct way to go about it? Thanks!
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.