½ = 1/x² + 1/y² +...+ 1/z²

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

There is an infinite solution I found using the following variables:

2,3,4,6,12,5^1,5^2,5^3,5^4,5^5...

However, I don't think there is a finite solution.  It just doesn't seem likely.