Tính tổng: A=3+3 ² +3 ³+…3 ∧100 B=3^2011-3^2010+…+3 ³-3 ²+3-1 31/10/2021 Bởi Madelyn Tính tổng: A=3+3 ² +3 ³+…3 ∧100 B=3^2011-3^2010+…+3 ³-3 ²+3-1
Đáp án: @Kudo `A=3+3^2+3^3+…+3^(100)` `=>3A=3^2+3^3+3^4+…+3^(101)` `=>3A-A=3^2+3^3+3^4+…+3^(101)-3-3^2-3^3-…-3^(100)` `=>2A=3^(101)-3` `=>A=(3^(101)-3)/2` `B=3^(2011)-3^(2010)+…+3^3-3^2+3-1` `=>3B=3^(2012)-3^(2011)+…+3^4-3^3+3^2-3` `=>3B+B=3^(2012)-3^(2011)+…+3^4-3^3+3^2-3+3^(2011)-3^(2010)+…+3^3-3^2+3-1` `=>4B=3^(2012)-1` `=>B=(3^(2012)-1)/4` Giải thích các bước giải: Bình luận
Đáp án : `A=(3^(101)-3)/2` `B=(3^(2012)-1)/4` Giải thích các bước giải : `A=3+3^2+3^3+…+3^(100)` `<=>3A=3^2+3^3+3^4+…+3^(101)` `<=>3A-A=3^2+3^3+3^4+…+3^(101)-3-3^2-3^3-…-3^(100)` `<=>2A=3^(101)-3` `<=>A=(3^(101)-3)/2` Vậy `A=(3^(101)-3)/2` `B=3^(2011)-3^(2010)+…+3^3-3^2+3-1` `<=>3B=3^(2012)-3^(2011)+…+3^4-3^3+3^2-3` `<=>3B+B=3^(2012)-3^(2011)+…+3^4-3^3+3^2-3+3^(2011)-3^(2010)+…+3^3-3^2+3-1` `<=>4B=3^(2012)-1` `<=>B=(3^(2012)-1)/4` Vậy `B=(3^(2012)-1)/4` Bình luận
Đáp án:
@Kudo
`A=3+3^2+3^3+…+3^(100)`
`=>3A=3^2+3^3+3^4+…+3^(101)`
`=>3A-A=3^2+3^3+3^4+…+3^(101)-3-3^2-3^3-…-3^(100)`
`=>2A=3^(101)-3`
`=>A=(3^(101)-3)/2`
`B=3^(2011)-3^(2010)+…+3^3-3^2+3-1`
`=>3B=3^(2012)-3^(2011)+…+3^4-3^3+3^2-3`
`=>3B+B=3^(2012)-3^(2011)+…+3^4-3^3+3^2-3+3^(2011)-3^(2010)+…+3^3-3^2+3-1`
`=>4B=3^(2012)-1`
`=>B=(3^(2012)-1)/4`
Giải thích các bước giải:
Đáp án :
`A=(3^(101)-3)/2`
`B=(3^(2012)-1)/4`
Giải thích các bước giải :
`A=3+3^2+3^3+…+3^(100)`
`<=>3A=3^2+3^3+3^4+…+3^(101)`
`<=>3A-A=3^2+3^3+3^4+…+3^(101)-3-3^2-3^3-…-3^(100)`
`<=>2A=3^(101)-3`
`<=>A=(3^(101)-3)/2`
Vậy `A=(3^(101)-3)/2`
`B=3^(2011)-3^(2010)+…+3^3-3^2+3-1`
`<=>3B=3^(2012)-3^(2011)+…+3^4-3^3+3^2-3`
`<=>3B+B=3^(2012)-3^(2011)+…+3^4-3^3+3^2-3+3^(2011)-3^(2010)+…+3^3-3^2+3-1`
`<=>4B=3^(2012)-1`
`<=>B=(3^(2012)-1)/4`
Vậy `B=(3^(2012)-1)/4`