c:=500  (* c is actually going to Infinity  *)

tech:=Pi^2/6

zr2:=Sum[Sum[1/((k-r)*k) , {r,0,k-1}] , {k,0,c}]
zr3:=Sum[Sum[1/((k-r)*k) , {r,1,k-1}] , {k,1,c}]

result:=zr2-zr3

N[tech]
N[result]

1.64493
1.6429360655148942

    Source: geocities.com/timeparadox