Toán CMR:3/1².2 ² + 5/2².3² +7/3².4² +19/9².10² <1 22/11/2021 By Faith CMR:3/1².2 ² + 5/2².3² +7/3².4² +19/9².10² <1
Đáp án: `đpcm` Giải thích các bước giải: `3/(1^2 . 2^2)+5/(2^2 . 3^2) +…+19/(9^2 . 10^2)` `= (2^2-1^2)/(1^2 . 2^2)+(3^2-2^2)/(2^2 . 3^2)+…+(10^2-9^2)/(9^2. 10^2)` `=2^2/(1^2. 2^2)-1^2/(1^2. 2^2)+3^2/(2^2. 3^2)+…+10^2/(9^2. 10^2)-9^2/(9^2. 10^2)` `=1/1-1/2^2+1/2^2-1/3^2+1/3^2-1/4^2+…+1/9^2-1/10^2` `=1-1/10^2<1` `=> đpcm` Trả lời
`A=3/(1^2 .2^2)+5/(2^2 .3^2)+7/(3^2 .4^2)+…+19/(9^2 .10^2)` `=3/(1.4)+5/(4.9)+7/(9.16)+…+19/(81.100)` `=1-1/4+1/4-1/9+1/9-1/16+…+1/81-1/100` `=1-1/100 <1` `→ĐPCM` Trả lời
Đáp án:
`đpcm`
Giải thích các bước giải:
`3/(1^2 . 2^2)+5/(2^2 . 3^2) +…+19/(9^2 . 10^2)`
`= (2^2-1^2)/(1^2 . 2^2)+(3^2-2^2)/(2^2 . 3^2)+…+(10^2-9^2)/(9^2. 10^2)`
`=2^2/(1^2. 2^2)-1^2/(1^2. 2^2)+3^2/(2^2. 3^2)+…+10^2/(9^2. 10^2)-9^2/(9^2. 10^2)`
`=1/1-1/2^2+1/2^2-1/3^2+1/3^2-1/4^2+…+1/9^2-1/10^2`
`=1-1/10^2<1`
`=> đpcm`
`A=3/(1^2 .2^2)+5/(2^2 .3^2)+7/(3^2 .4^2)+…+19/(9^2 .10^2)`
`=3/(1.4)+5/(4.9)+7/(9.16)+…+19/(81.100)`
`=1-1/4+1/4-1/9+1/9-1/16+…+1/81-1/100`
`=1-1/100 <1`
`→ĐPCM`