Đáp án:
`1+1/3+1/9+1/27+1/81+1/243+1/729=1093/729`
Giải thích các bước giải:
`1+1/3+1/9+1/27+1/81+1/243+1/729`
`=1+1/3+1/3^2+1/3^3+1/3^4+1/3^5+1/3^6`
Đặt `A=1+1/3+1/3^2+1/3^3+1/3^4+1/3^5+1/3^6`
`3A=3.(1+1/3+1/3^2+1/3^3+1/3^4+1/3^5+1/3^6)`
`3A=3+1+1/3+1/3^2+1/3^3+1/3^4+1/3^5`
`3A-A=(4+1/3+1/3^2+1/3^3+1/3^4+1/3^5)-(1+1/3+1/3^2+1/3^3+1/3^4+1/3^5+1/3^6)`
`2A=4+1/3+1/3^2+1/3^3+1/3^4+1/3^5-1-1/3-1/3^2-1/3^3-1/3^4-1/3^5-1/3^6`
`2A=(4-1)+(1/3-1/3)+(1/3^2-1/3^2)+(1/3^3-1/3^3)+(1/3^4-1/3^4)+(1/3^5-1/3^5)-1/3^6`
`2A=3-1/3^6`
`A=(3-1/3^6)/2`
`A=(3-1/729)/2`
`A=(2187/729-1/729) /2`
`A=2186/729 . 1/2`
`A=2186/1458`
`A=1093/729`
Vậy `1+1/3+1/9+1/27+1/81+1/243+1/729=1093/729`
