½ = 1/x² + 1/y² +...+ 1/z²

All variables must be different, positive integers, and there must be a finite number of terms.

Well done e.g.  Great to see a solution derived by a non-number cruncher. 

I checked your answer by converting each fraction to 90,000ths (1/300^2) and sure enough the sum was 45,000/90,000.

Great puzzle Federico.