Toán Cho A= 1+ 3+ 3^2+3^4+3^5+…+ 3^31. chứng minh A chia hết cho 13 18/11/2021 By Eva Cho A= 1+ 3+ 3^2+3^4+3^5+…+ 3^31. chứng minh A chia hết cho 13
$A = 1+3+3^2+3^4+3^5+…+3^{31}$ $A = (1+3+3^2) + (3^4+3^5+3^6) + …. + (3^{29} + 3^{30} + 3^{31})$ $A = 1(1+ 3 + 3^2) + 3^4(1+3+3^2) + … + 3^{29}(1+3+3^2)$ $A = 1 . 13 + 3^4 . 13 + … + 3^{29} . 13$ `A = 13(1+3^4 + … +3^{29}) \vdots 13` Trả lời
$A = 1+3+3^2+3^4+3^5+…+3^{31}$
$A = (1+3+3^2) + (3^4+3^5+3^6) + …. + (3^{29} + 3^{30} + 3^{31})$
$A = 1(1+ 3 + 3^2) + 3^4(1+3+3^2) + … + 3^{29}(1+3+3^2)$
$A = 1 . 13 + 3^4 . 13 + … + 3^{29} . 13$
`A = 13(1+3^4 + … +3^{29}) \vdots 13`