A=7+7²+7³+...+7²⁰¹⁶

=(7+7²)+(7³+7⁴)+...+(7²⁰¹⁵+7²⁰¹⁶)

=7.(1+7)+7³.(1+8)+...+7²⁰¹⁵.(1+7)

=7.8+7³.8+...+7²⁰¹⁵.8

=8.(7+7³+...+7²⁰¹⁵) chia hết cho 8 (đpcm)

A=7+7²+7³+...+7²⁰¹⁶

=(7+7²+7³)+...+(7²⁰¹⁴+7²⁰¹⁵+7²⁰¹⁶)

=7.(1+7+7²)+...+7²⁰¹⁴.(1+7+7²)

=7.57+...+7²⁰¹⁴.57

=57.(7+...+7²⁰¹⁴) chia hết cho 57 (đpcm)

\(A=7+7^2+7^3+...+7^{2016}\)

\(A=\left(7+7^2+7^3\right)+\left(7^4+7^5+7^6\right)+...+\left(7^{2014}+7^{2015}+7^{2016}\right)\)

\(A=7\left(1+7+7^2\right)+7^4\left(1+7+7^2\right)+...+7^{2014}\left(1+7+7^2\right)\)

\(A=7.57+7^4.57+...+7^{2014}.57\)

\(A=\left(7+7^4+...+7^{2014}\right).57⋮57\) ( đpcm ) 

Ta có :

\(A=7\left(1+7+7^2\right)+.....+7^{2014}\left(1+7+7^2\right)\)

\(\Rightarrow A=7.57+....+7^{2014}.57\)

\(\Rightarrow A=57.\left(7+....+7^{2014}\right)\)

=> A chia hêt cho 57

a+5b ⋮ 7
=> 3(a+5b) ⋮7
=> 3a+15b⋮7
=> 3a+15b +7a -14b⋮7
=> 10a+b⋮7
chúc bn hok tốt ^_^

              A = 7 + 7² + 7³ + .... + 7²⁰¹⁶        có (2016 - 1) : 1 + 1 = 2016 số hạng

             A = (7 + 7² + 7³) + ... + (7²⁰¹⁴ + 7²⁰¹⁵ + 7²⁰¹⁶)

            A = 7 . (1 + 7 + 7²) + .... + 7²⁰¹⁴ . (1 + 7 + 7²)

            A = 7 . (1 + 7 + 49) + .... + 7²⁰¹⁴ . (1 + 7+ 49)

           A = 7 . 57 + ... + 7²⁰¹⁴ . 57

           A = 57 . (7 + ... + 7²⁰¹⁴) chia hết cho 57

         => A chia hết cho 57 (ĐPCM)

        Ủng hộ mk nha !!! ^_^

A = 7 + 7² + 7³ +.....+ 7²⁰¹⁶

A = (7 + 7² + 7³) + (7⁴ + 7⁵ + 7⁶) +....+ (7²⁰¹⁴ + 7²⁰¹⁵ + 7²⁰¹⁶)

A = 7(1+7+7²) + 7⁴(1+7+7²) +....+ 7²⁰¹⁴(1+7+7²)

A = 7.57 + 7⁴.57 +.....+ 7²⁰¹⁴.57

A = (7 + 7⁴ +....+ 7²⁰¹⁴).57 chia hết cho 57 (Đpcm)

S = \(7+7^2+.............+7^{2016}\)

\(7S=7^2+7^3+...........+7^{2017}\)

\(7S-S=\left(7^2-7^2\right)+\left(7^3-7^3\right)+...........+7^{2017}-7\)

\(S=\frac{7^{2017}-7}{6}\)

b) \(S=\left(7+7^2+7^3+7^4\right)+.............+\left(7^{2013}+7^{2014}+7^{2015}+7^{2016}\right)\)

\(S=35.2^4.5+35.2^4.5.7^4+.........+35.2^4.5.7^{2012}\)

\(S=35.2^4.5.\left(1+7^4+7^8+............+7^{2012}\right)\)

Vậy chia hết cho 35          

đề đúng không vậy Nguyễn Tuấn Tài