Ta có:
1/41 + 1/42 + .....+1/60 < 1/40 . 20 = 1/2
1/61 + 1/62 +.......+1/80 < 1/60 . 20 = 1/3
=> 1/41 + 1/42 +.....+1/79 + 1/80 < 1/2 + 1/3 = 5/6
1/41 + 1/42 +...+1/60 > 1/60 . 20 = 1/3
1/61 + 1/62 +....+ 1/80 > 1/80 . 20 = 1/4
=> 1/41 + 1/42 +.......+ 1/79 + 1/80 > 1/3 + 1/4 = 7/12
KL: Vậy 7/12 < 1/41 + 1/42 +.....+ 1/80 < 5/6 (đpcm)