Question

[⚽๖ۣۜTrần ๖ۣۜQuốc🏆๖ۣۜDũng🥇||✅]

Cho A = 3¹ + 3² + 3³ + .....+ 3²⁰¹⁰

    ^{Chứng minh A chia hết cho 13}

Answer 1

[⚽Trần Quốc🏆Huy🥇]

A = 3¹ + 3² + 3³ + .....+ 3²⁰¹⁰

A = ( 3 + 3² + 3³ ) + .....+ ( 3²⁰⁰⁸ + 3²⁰⁰⁹ +  3²⁰¹⁰ )

A = 3 x ( 1 + 3 + 3² ) + .....+ 3²⁰⁰⁸ x ( 1 + 3 + 3² )

A = 3 x 13 + ..... + 3²⁰⁰⁸ x 13

A = 13 x ( 3 + ... + 3^{2008 )}

           Vậy A \(⋮\)cho 13

Answer 2

[Khánh Ngọc]

\(A=3^1+3^2+3^3+...+3^{2010}\)

\(\Rightarrow A=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+...+\left(3^{2008}+3^{2009}+3^{2010}\right)\)

\(\Rightarrow A=3\left(1+3+3^2\right)+3^4\left(1+3+3^2\right)+...+3^{2008}\left(1+3+3^2\right)\)

\(\Rightarrow A=13.\left(3+3^4+3^7+...+3^{2008}\right)⋮13\) ( đpcm )