chứng minh rằng: 1\41+1\42+1\43+…….+1\78+1\80>7\12 22/09/2021 Bởi Isabelle chứng minh rằng: 1\41+1\42+1\43+…….+1\78+1\80>7\12
Đáp án + Giải thích các bước giải: `1/41+1/42+…+1/79+1/80` `=(1/41+1/42+…+1/60)+(1/61+1/62+…+1/80)` Ta có : `1/41>1/60 ; 1/42>1/60 ; … 1/59>1/60 ` `\to 1/41+1/42+…+1/60>1/60+1/60+…+1/60=20/60=1/3` Lại có : `1/61>1/80 ; 1/62>1/80 ; …. ; 1/79>1/80 ` `\to 1/61+1/62+…+1/80>1/80+1/80+…+1/80=20/80=1/4` `\to 1/41+1/42+…+1/60)+(1/61+1/62+…+1/80)>1/3+1/4=7/12` Vậy `1/41+1/42+…+1/79+1/80>7/12` Bình luận
Đáp án + Giải thích các bước giải:
`1/41+1/42+…+1/79+1/80`
`=(1/41+1/42+…+1/60)+(1/61+1/62+…+1/80)`
Ta có : `1/41>1/60 ; 1/42>1/60 ; … 1/59>1/60 `
`\to 1/41+1/42+…+1/60>1/60+1/60+…+1/60=20/60=1/3`
Lại có : `1/61>1/80 ; 1/62>1/80 ; …. ; 1/79>1/80 `
`\to 1/61+1/62+…+1/80>1/80+1/80+…+1/80=20/80=1/4`
`\to 1/41+1/42+…+1/60)+(1/61+1/62+…+1/80)>1/3+1/4=7/12`
Vậy `1/41+1/42+…+1/79+1/80>7/12`