[lmikle]

Как-то так:

Код:

function TForm1.SumFx(X : Double) : Double;
var
  dX : Double;
  K : Integer;
begin
  Result := Fxi(X,0);
  K := 0;
  While (True) Do
    Begin
      Inc(K);
      dX := Fxi(X,K);
      If Result = Result + dX Then Break;
      Result := Result + dX;
      If K > 1000000 Then Break;
    End;
end;

function TForm1.Fxi(X : Double; I : Integer) : Double;
begin
  Result := X / (I*I*I + I*Sqrt(Abs(X))+1);
end;