8/9>A>2/5 Cho A=1/2:2 +1/3:3+1/4:4+…+1/9:9 29/08/2021 Bởi Madeline 8/9>A>2/5 Cho A=1/2:2 +1/3:3+1/4:4+…+1/9:9
Ta có: `1/2.2 < 1/1.2 ; 1/3.3 < 1/2.3; ….. ; 1/9.9 < 1/8.9` `=> 1/2.2 + 1/3.3 + 1/4.4+………+ 1/9.9 < 1/1.2 + 1/2.3 + …. + 1/8.9` `=> A < 1/1 -1/2 + 1/2 -1/3 +….+ 1/8- 1/9` `=>A < 1/1 -1/9` `=> A < 8/9 (1)` Lại có: `1/2.2 > 1/2.3 ; 1/3.3 > 1/3.4 ; ………; 1/9.9> 1/9.10` `=> 1/2.2 + 1/3.3 + 1/4.4+………+ 1/9.9> 1/2.3 + 1/3.4 +…+ 1/9.10` `=> A > 1/2 -1/3 + 1/3 -1/4 +….+ 1/9-1/10` `=> A > 1/2 -1/10 = 2/5(2)` Từ `(1)` và `(2)` `=> 8/9 > A > 2/5` Vậy `8/9 > A > 2/5` Bình luận
Ta có: `1/2.2 < 1/1.2 ; 1/3.3 < 1/2.3; ….. ; 1/9.9 < 1/8.9`
`=> 1/2.2 + 1/3.3 + 1/4.4+………+ 1/9.9 < 1/1.2 + 1/2.3 + …. + 1/8.9`
`=> A < 1/1 -1/2 + 1/2 -1/3 +….+ 1/8- 1/9`
`=>A < 1/1 -1/9`
`=> A < 8/9 (1)`
Lại có: `1/2.2 > 1/2.3 ; 1/3.3 > 1/3.4 ; ………; 1/9.9> 1/9.10`
`=> 1/2.2 + 1/3.3 + 1/4.4+………+ 1/9.9> 1/2.3 + 1/3.4 +…+ 1/9.10`
`=> A > 1/2 -1/3 + 1/3 -1/4 +….+ 1/9-1/10`
`=> A > 1/2 -1/10 = 2/5(2)`
Từ `(1)` và `(2)` `=> 8/9 > A > 2/5`
Vậy `8/9 > A > 2/5`
Thân gửi bạn!