Tham khảo
Đặt `A=\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{20}}`
`⇒2A=1+\frac{1}{2}+...+\frac{1}{2^{19}}`
`⇒2A-A=1+\frac{1}{2}+...+\frac{1}{2^{19}}-(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{20}})`
`⇒A=1-\frac{1}{2^{20}}<1`(*)
Mà `B=\frac{-212121}{-202020}=\frac{-21}{-20}=\frac{21}{20}>1`(**)
Từ (*),(**)`⇒A<B`
`\text{©CBT}`