Add a condition to the double summation

Question

How can I add this condition

Ei[i] + Ei[j] != 0

to the following summation?

Sum[ (2 Ei[i] Ei[j])/(Ei[i] + Ei[j]), {j, 1, 4}, {i, 1, 4} ]

Answer 1

One way might be to add an If inside the Sum

Ei[1] = 1; Ei[2] = 2; Ei[3] = -1; Ei[4] = 5;
Sum[(2 Ei[i] Ei[j])/(Ei[i] + Ei[j]), {j, 1, 4}, {i, 1, 4}]

Replace with

Sum[den = (Ei[i] + Ei[j]); 
 If[den != 0, (2 Ei[i] Ei[j])/den, 0], {j, 1, 4}, {i, 1, 4}]

(*40/7*)