Thanks guys. I wanted to know if it converges and it does, but I proved it without wolfram…
It's a finite sum, so I'm not sure what you mean by convergence. Have you seen this?:
SumConvergence[i^(-a)*j^(-a - 1), {i, j}] (* Re[a] > 1 *)
Perhaps that's what you wanted.
Try with a noninteger value of a
a
With[{a = 1/2}, Sum[i^(-a)*j^(-a - 1), {i, 1, n}, {j, i + 1, n}]]
If that gives no closed form, then there is little hope for symbolic a.
