Summation with inequalities

Question

How can I perform this function with Mathematica?

$$\sum_{1\le j<k\le N}\frac1{\left(r_{jk}\right)^\alpha}$$

where n = 5.

Answer 1

n = 5;
Sum[1/r[j, k]^α, {k, 1, n}, {j, 1, k - 1}]

r[1, 2]^-α + r[1, 3]^-α + r[1, 4]^-α + r[1, 5]^-α + r[2, 3]^-α + r[2, 4]^-α +
r[2, 5]^-α + r[3, 4]^-α + r[3, 5]^-α + r[4, 5]^-α

Alternatively,

Sum[Boole[1 <= j < k <= n]/r[j, k]^α, {j, 1, n}, {k, 1, n}]

r[1, 2]^-α + r[1, 3]^-α + r[1, 4]^-α + r[1, 5]^-α + r[2, 3]^-α + r[2, 4]^-α +
r[2, 5]^-α + r[3, 4]^-α + r[3, 5]^-α + r[4, 5]^-α