Toán So sanh S với 3 biết : S = 2019/2020 + 2020/2021 + 2021/2019 17/07/2021 By Arya So sanh S với 3 biết : S = 2019/2020 + 2020/2021 + 2021/2019
`S=2019/2020+2020/2021+2021/2019` `=(1-1/2020)+(1-1/2021)+(1+2/2019)` `=1-1/2020+1-1/2021+1+2/2019` `=1+1+1-1/2020-1/2021+2/2019` `=3-1/2020-1/2021+2/2019` `=3+(2/2019-1/2020-1/2021)` Vì: `1/2020;1/2021<1/2019` `⇒1/2019+1/2019>1/2020+1/2021` `⇒2/2019>1/2020+1/2021` `⇒2/2019-(1/2020+1/2021)>0` `⇒2/2019-1/2020-1/2021)>0` `⇒S>3+0` `⇒S>3` Trả lời
Đáp án+Giải thích các bước giải: `S-3=(2019/2020 +2020/2021 +2021/2019)-3`$\\$`=(2019/2020-1)+(2020/2021-1)+(2021/2019-1)`$\\$`=-1/2020-1/2021+2/2019`$\\$`=(1/2019-1/2020)+(1/2019-1/2021)>0`$\\$`=>2019/2020 +2020/2021 +2021/2019>3` Trả lời
`S=2019/2020+2020/2021+2021/2019`
`=(1-1/2020)+(1-1/2021)+(1+2/2019)`
`=1-1/2020+1-1/2021+1+2/2019`
`=1+1+1-1/2020-1/2021+2/2019`
`=3-1/2020-1/2021+2/2019`
`=3+(2/2019-1/2020-1/2021)`
Vì: `1/2020;1/2021<1/2019`
`⇒1/2019+1/2019>1/2020+1/2021`
`⇒2/2019>1/2020+1/2021`
`⇒2/2019-(1/2020+1/2021)>0`
`⇒2/2019-1/2020-1/2021)>0`
`⇒S>3+0`
`⇒S>3`
Đáp án+Giải thích các bước giải:
`S-3=(2019/2020 +2020/2021 +2021/2019)-3`$\\$`=(2019/2020-1)+(2020/2021-1)+(2021/2019-1)`$\\$`=-1/2020-1/2021+2/2019`$\\$`=(1/2019-1/2020)+(1/2019-1/2021)>0`$\\$`=>2019/2020 +2020/2021 +2021/2019>3`