Rút gọn C = 1/3 + 1/3^4 + 1/3^7 + 1/3^10 + 1/3^13

Đáp án+Giải thích các bước giải:

`  C = 1/3 + 1/3^4 + 1/3^7 + 1/3^10 + 1/3^13`
`3^3C=(1/3 + 1/3^4 + 1/3^7 + 1/3^10 + 1/3^13).3^3`
`27C=3^3/3 + 3^3/3^4 + 3^3/3^7 + 3^3/3^10 + 3^3/3^13`
`27C=3^2+1/3+1/3^4+1/3^7+1/3^10`
`27C-C=(3^2+1/3+1/3^4+1/3^7+1/3^10)-(1/3 + 1/3^4 + 1/3^7 + 1/3^10 + 1/3^13)`
`26C=3^2-1/3^13`
`26C=9-1/3^13`
`C=[9-1/3^13]/26`

Vậy `C=[9-1/3^13]/26`

`C = 1/3 + 1/3^4 + 1/3^7 + 1/3^{10} + 1/3^{13}`

`=> 3^3 C = 3^2 + 1/3 + 1/3^4 + 1/3^7 + 1/3^{10}`

`=> 27C - C = ( 9 + 1/3 + 1/3^4 + 1/3^7 + 1/3^{10} ) - ( 1/3 + 1/3^4 + 1/3^7 + 1/3^{10} + 1/3^{13} )`

`=> 26C = 9 - 1/3^{13}`

`=> C = 9/26 - 1/( 26 . 3^{13} )`

Vậy `: C = 9/26 - 1/( 26 . 3^{13} )`