(2000^2001)/(2001^2000)
＝(2000^2000×2000)/(2001^2000)
＝(2000/2001)^2000×2000
＝[(2000/2001)^1000]^2×2000
＞[(2000/2001)×(1999/2000)×(1998/1999)×...×(1002/1003)×(1001/1002)]^2×2000
＝(1001/2001)^2×2000
＞(1000/2000)^2×2000
＝1/4×2000
＞1
∴2000^2001＞2001^2000