Question

[nguienphucanhtri]

Cho A=2+2²+2³+.......+2²⁰¹⁷+2²⁰¹⁸

^{Tim so du khi chia A cho 3}

Answer 1

[Newton]

A= 2 + 2² + 2³ + ................+ 2²⁰¹⁷ + 2²⁰¹⁸

\(\Rightarrow\)A= ( 2 + 2² ) +( 2³ + 2⁴ ) +......................+ ( 2²⁰¹⁷  + 2²⁰¹⁸ ) 

\(\Rightarrow\)A= 6 + 2² x (2 +2²  ) + ..............2²⁰¹⁶ x ( 2 + 2² )

\(\Rightarrow\)A= 6+ 2² x 6 + .................2²⁰¹⁶ x 6 

\(\Rightarrow\)A= 6 x ( 1+ 2² + ........2²⁰¹⁶ )

Vì 6 \(⋮\)3 \(\Rightarrow\)6 x ( 1+ 2² + ........2²⁰¹⁶ ) \(⋮\)3

\(\Rightarrow\)\(\Rightarrow\)A \(⋮\)3

Vậy A \(⋮\)3

Answer 2

[nguienphucanhtri]

To lai cho khi cac cau cha loi dung