Define new coefficients
beta i = alpha i/sum alpha
to get a production function of the form
(sum alpha)^(1/rho)* CES with coefficients beta i summing to one. If you now let rho tend to zero, the limit either collapses to zero for sum alpha < 1, stays the same for sum alpha =1 or diverges for sum alpha > 1.

All the examples I have seen in the book have sum alpha = 2 but this is not a problem unless you want to start looking at what happens for limiting values of rho.