C= 2 mũ 100 trừ 2 mũ 99 trừ 2 mũ 98 trừ …..trừ 2 mũ 2 trừ 2 trừ 1 26/10/2021 Bởi Valentina C= 2 mũ 100 trừ 2 mũ 99 trừ 2 mũ 98 trừ …..trừ 2 mũ 2 trừ 2 trừ 1
`C=2^100-2^99-2^98-2^97-…-2^2-2-1` `-> C= 2^100-(2^99+2^98+2^97+…+2^2+2+1)` – Đặt `D=2^99+2^98+2^97+…+2^2+2+1` `-> 2D= 2^100+2^99+2^98+…+2^3+2^2` `-> 2D-D=(2^100+2^99+2^98+…+2^3+2^2+2)-(2^99+2^98+2^97+…+2^2+2+1)` `-> D=2^100-1` – Ta có : `C=2^100-D` `-> C=2^100-(2^100-1)` `-> C=2^100-2^100+1` `-> C=1` Bình luận
`C=2^100-2^99-2^98-2^97-…-2^2-2-1`
`-> C= 2^100-(2^99+2^98+2^97+…+2^2+2+1)`
– Đặt `D=2^99+2^98+2^97+…+2^2+2+1`
`-> 2D= 2^100+2^99+2^98+…+2^3+2^2`
`-> 2D-D=(2^100+2^99+2^98+…+2^3+2^2+2)-(2^99+2^98+2^97+…+2^2+2+1)`
`-> D=2^100-1`
– Ta có : `C=2^100-D`
`-> C=2^100-(2^100-1)`
`-> C=2^100-2^100+1`
`-> C=1`
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