Câu hỏi cuối nhé! Tính `1-1/3-1/9-1/27+1/81-…+1/6561-1/19683` 18/08/2021 Bởi Vivian Câu hỏi cuối nhé! Tính `1-1/3-1/9-1/27+1/81-…+1/6561-1/19683`
Đặt ` A = 1 – 1/3 + 1/9 – 1/27 + 1/81 – …. + 1/6561 – 1/19683` `A = 1 – 1/3 + 1/3^2 – 1/3^3 + 1/3^4 – … + 1/3^8 – 1/3^9` `3 . A = 3 – 1 + 1/3 – 1/3^2 + 1/3^3 – …. + 1/3^7 – 1/3^8` `3A + A = ( 3 – 1 + 1/3 – 1/3^2 + 1/3^3 – … + 1/3^7 – 1/3^8 ) + ( 1 – 1/3 + 1/3^2 – 1/3^3 + 1/3^4 – …. + 1/3^8 – 1/3^9 )` `4 . A = 3 – 1 + 1/3 – 1/3^2 + 1/3^3 – …. + 1/3^7 – 1/3^8 + 1 – 1/3 + 1/3^2 – 1/3^3 + 1/3^4 – …. + 1/3^8 – 1/3^9` `4 . A = 3 – 1/3^9` `4 . A = ( 3^10 – 1 )/3^9` `A = ( 3^10 – 1 )/3^9 : 4` `A = ( 3^10 – 1 )/( 3^9 . 4 )` Bình luận
Đáp án: Giải thích các bước giải: `M=1-1/3+1/9-1/27+1/81-…+1/6561-1/19683` `M=1-1/3+1/3^2-1/3^3+1/3^4-….+1/3^8-1/3^9` `=>3M=3-1+1/3-1/3^2+1/3^3-….+1/3^7-1/3^8` `=>3M+M=(3-1+1/3-1/3^2+1/3^3-….+1/3^7-1/3^8)+(1-1/3+1/3^2-1/3^3+1/3^4-….+1/3^8-1/3^9)` `=>4M=3-1/3^9` `=>M=(3-1/3^9)/4` `=>M=3/4 -1/(4.3^9)` Bình luận
Đặt ` A = 1 – 1/3 + 1/9 – 1/27 + 1/81 – …. + 1/6561 – 1/19683`
`A = 1 – 1/3 + 1/3^2 – 1/3^3 + 1/3^4 – … + 1/3^8 – 1/3^9`
`3 . A = 3 – 1 + 1/3 – 1/3^2 + 1/3^3 – …. + 1/3^7 – 1/3^8`
`3A + A = ( 3 – 1 + 1/3 – 1/3^2 + 1/3^3 – … + 1/3^7 – 1/3^8 ) + ( 1 – 1/3 + 1/3^2 – 1/3^3 + 1/3^4 – …. + 1/3^8 – 1/3^9 )`
`4 . A = 3 – 1 + 1/3 – 1/3^2 + 1/3^3 – …. + 1/3^7 – 1/3^8 + 1 – 1/3 + 1/3^2 – 1/3^3 + 1/3^4 – …. + 1/3^8 – 1/3^9`
`4 . A = 3 – 1/3^9`
`4 . A = ( 3^10 – 1 )/3^9`
`A = ( 3^10 – 1 )/3^9 : 4`
`A = ( 3^10 – 1 )/( 3^9 . 4 )`
Đáp án:
Giải thích các bước giải:
`M=1-1/3+1/9-1/27+1/81-…+1/6561-1/19683`
`M=1-1/3+1/3^2-1/3^3+1/3^4-….+1/3^8-1/3^9`
`=>3M=3-1+1/3-1/3^2+1/3^3-….+1/3^7-1/3^8`
`=>3M+M=(3-1+1/3-1/3^2+1/3^3-….+1/3^7-1/3^8)+(1-1/3+1/3^2-1/3^3+1/3^4-….+1/3^8-1/3^9)`
`=>4M=3-1/3^9`
`=>M=(3-1/3^9)/4`
`=>M=3/4 -1/(4.3^9)`