So sánh `1/2+2/3+3/4+…+2019/2020` và `5` 18/07/2021 Bởi Ximena So sánh `1/2+2/3+3/4+…+2019/2020` và `5`
Đáp án: `1/2+2/3+3/4+…+2019/2020>5` Giải thích các bước giải: `1/2+2/3+3/4+…+2019/2020` `=(2-1)/2+(3-1)/3+(4-1)/4+…+(2020-2019)/2020` `=1-1/2+1-1/3+1-1/4+…+1-1/2020` `=(1+1+1+…+1)-(1/2+1/3+1/4+…+1/2020)` `=2019-(1/2+1/3+1/4+…+1/2020)` Ta có: `1/2 + 1/3 + … + 1/2020 < 1/2 + 1/2 + 1/2 + … + 1/2 = 1/2. 2019 = 2019/2 = 1009,5` `⇒ – (1/2 + 1/3 + … + 1/2020) > – 1009,5` `⇒2019 – (1/2 + 1/3 + … + 1/2020) > 2019 – 1009,5 = 1009,5 > 5` `⇒ A>5` Vậy `A>5`. Bình luận
Đáp án: Giải thích các bước giải: Ta có : `1/2` + `2/3` + `3/4` + … + `2019/2020` = $\frac{2-1}{2}$ + $\frac{3-1}{3}$ + $\frac{4-1}{4}$ + … + $\frac{2020-1}{2020}$ = ( $\frac{2}{2}$ – $\frac{1}{2}$ ) + ( $\frac{3}{3}$ – $\frac{1}{3}$ ) + ( $\frac{4}{4}$ – $\frac{1}{4}$ ) + … + ( $\frac{2020}{2020}$ – $\frac{1}{2020}$ ) = `1/1` – `1/2` + `1/1` – `1/3` + `1/1` – `1/4` + ….. + `1/1` – `1/2020` = `1/1` – `1/2020` `<` 5. Vậy `1/2` + `2/3` + `3/4` + … + `2019/2020` `<` `5` Bình luận
Đáp án: `1/2+2/3+3/4+…+2019/2020>5`
Giải thích các bước giải:
`1/2+2/3+3/4+…+2019/2020`
`=(2-1)/2+(3-1)/3+(4-1)/4+…+(2020-2019)/2020`
`=1-1/2+1-1/3+1-1/4+…+1-1/2020`
`=(1+1+1+…+1)-(1/2+1/3+1/4+…+1/2020)`
`=2019-(1/2+1/3+1/4+…+1/2020)`
Ta có:
`1/2 + 1/3 + … + 1/2020 < 1/2 + 1/2 + 1/2 + … + 1/2 = 1/2. 2019 = 2019/2 = 1009,5`
`⇒ – (1/2 + 1/3 + … + 1/2020) > – 1009,5`
`⇒2019 – (1/2 + 1/3 + … + 1/2020) > 2019 – 1009,5 = 1009,5 > 5`
`⇒ A>5`
Vậy `A>5`.
Đáp án:
Giải thích các bước giải:
Ta có :
`1/2` + `2/3` + `3/4` + … + `2019/2020`
= $\frac{2-1}{2}$ + $\frac{3-1}{3}$ + $\frac{4-1}{4}$ + … + $\frac{2020-1}{2020}$
= ( $\frac{2}{2}$ – $\frac{1}{2}$ ) + ( $\frac{3}{3}$ – $\frac{1}{3}$ ) + ( $\frac{4}{4}$ – $\frac{1}{4}$ ) + … + ( $\frac{2020}{2020}$ – $\frac{1}{2020}$ )
= `1/1` – `1/2` + `1/1` – `1/3` + `1/1` – `1/4` + ….. + `1/1` – `1/2020`
= `1/1` – `1/2020` `<` 5.
Vậy `1/2` + `2/3` + `3/4` + … + `2019/2020` `<` `5`