\(A=2+2^2+2^3+2^4+...+2^7+2^8+2^9+2^{10}\)
\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^9+2^{10}\right)\)
\(A=1.\left(2+2^2\right)+2^2\left(2+2^2\right)+...+2^8.\left(2+2^2\right)\)
\(A=1.6+2^2.6+...+2^8.6\)
\(A=6\left(1+2^2+...+2^8\right)\)
Mà \(6⋮3\Rightarrow6.\left(1+2^2+...+2^8\right)\)
\(\Rightarrow A⋮3\)
NHỚ **** nhé!!!
A = ( 2 + 2^2 ) + ( 2 ^ 3 + 2 ^ 4 ) + ( 2 ^ 5 + 2 ^ 6 ) + .......+ ( 2 ^ 9 + 2 ^ 10 )
= ( 2 .1 + 2 .2 ) + ( 2 ^ 3 . 1 + 2 ^ 3 . 2 ) + ........+ ( 2 ^ 9 . 1 + 2 ^ 9 . 2 )
= 2 . ( 1 + 2 ) + 2 ^ 3 . ( 1 + 2 ) + .........+ 2 ^ 9 . ( 1 + 2 )
= 2 . 3 + 2 ^ 3 . 3 + ....... + 2 ^ 9 . 3
= 3 . ( 2 + 2 ^ 3 + ..... + 2 ^ 9 ) chia hết cho 3
\(\Rightarrow\) A chia hêt cho 3
A=2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^10
A=(2+2^2)+2^2.(2+2^2)+2^4.(2+2^2)+2^6.(2+2^2)+2^8.(2+2^2)
A=6+2^2.6+2^4.6+2^6.6+2^8.6
A=(1+2^2+2^4+2^6+2^8).6
Vì 6 chia hết cho 3 nên A chia hết cho 3.
P/s : Học vui^^doan thi khanh linh ơi!
P/s là gì vậy ?