Question

Cho A=7³+7⁴+7⁵+7⁶+.........+7⁹⁷+7⁹⁸. Chứng tỏ A chia hết cho 8.

 

Answer 1

\(A=7^3+7^4+7^5+...+7^{97}+7^{98}\)

\(=\left(7^3+7^4\right)+\left(7^5+7^6\right)+\left(7^7+7^8\right)+...+\left(7^{97}+7^{98}\right)\)

\(=7^3\left(1+7\right)+7^5\left(1+7\right)+7^7\left(1+7\right)+...+7^{97}\left(1+7\right)\)

\(=8\left(7^3+7^5+7^7+...+7^{97}\right)\)  \(⋮8\)      (đpcm)

Answer 2

Ta có :

A = 7³ + 7⁴ + 7⁵ + 7⁶ +........+7⁹⁷ + 7⁹⁸

=> A = 7³ ( 1+ 7)+...........+7⁹⁷ ( 1+7)

=> A = 7³ x 8 +.......+7⁹⁸ x 8

=> A chia hết cho 8