Worksheet.Range(Cells(r,c),Cells(r,c)) & error 1004

I'd like to access a range using this syntax, but it never works!
Here's (the edited hightlights of) my code:

Sub Test()
  Set TestSheet = Worksheets("A")
  Set OutputSheet = Worksheets("B")
  For i = 1 To 10
    TestSheet.Range(Cells(i, 1), Cells(i, 6)).Copy
    OutputSheet.Cells(i, 1).Paste
  Next i
End Sub

When it gets to the bold line, the dreaded incomprehensible error 1004 strikes. It's very frustrating to be thwarted doing something so apparently simple... If anyone can explain what I'm doing wrong, I'll be very grateful!