Cho S=1+1/2+1/3+1/4+……+1/2^2017 Chứng minh S>1009 02/07/2021 Bởi Valentina Cho S=1+1/2+1/3+1/4+……+1/2^2017 Chứng minh S>1009
`S=1+1/2+1/3+1/4+……+1/2^2017` `Vì` `1>1/2;1/3;1/4;…;1/2^2017` `⇒S>\underbrace{1+1+1+…+1}_{2^2017\text{chữ số}}` `⇒S>2^2017>1009` `⇒S>1009` Bình luận
`S=1+1/2+1/3+1/4+……+1/2^2017`
`Vì` `1>1/2;1/3;1/4;…;1/2^2017`
`⇒S>\underbrace{1+1+1+…+1}_{2^2017\text{chữ số}}`
`⇒S>2^2017>1009`
`⇒S>1009`