Đáp án + Giải thích các bước giải:
Ta có: `1/41 + 1/42+1/43+...+1/79+1/80 = (1/41+1/42+1/43+...+1/60)+(1/61+1/62+...+1/80)`
+)
`@` `1/41+1/42+1/43+...+1/60 > 1/60+1/60+1/60+...+1/60 = 20/60 = 1/3`
`@` `1/61+1/62+1/63+...+1/80 > 1/80+1/80+1/80+...+1/80=20/80=1/4`
`→ (1/41+1/42+1/43+...+1/60)+(1/61+1/62+...+1/80) > 1/3+1/4 = 7/12\ (1)`
+)
`@` `1/41+1/42+1/43+...+1/60 < 1/40+1/40+1/40+...+1/40 = 20/40 = 1/2`
`@` `1/61+1/62+1/63+...+1/80 < 1/60+1/60+1/60+...+1/60 = 20/60 = 1/3`
`→(1/41+1/42+1/43+...+1/60)+(1/61+1/62+...+1/80) < 1/2+1/3=5/6 < 1\ (2)`
Từ `(1)(2)→7/12<1/41 + 1/42+1/43+...+1/79+1/80<1` (đpcm)