Question

cho số A=2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^10

chứng tỏ số A trên chia hết cho 3

giúp tớ với !!!

Answer 1

\(A=2+2^2+2^3+2^4+...+2^7+2^8+2^9+2^{10}\)

\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^9+2^{10}\right)\)

\(A=1.\left(2+2^2\right)+2^2\left(2+2^2\right)+...+2^8.\left(2+2^2\right)\)

\(A=1.6+2^2.6+...+2^8.6\)

\(A=6\left(1+2^2+...+2^8\right)\)

Mà \(6⋮3\Rightarrow6.\left(1+2^2+...+2^8\right)\)

\(\Rightarrow A⋮3\)

NHỚ **** nhé!!!

Answer 2

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

   

Answer 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^^ 

Answer 4

doan thi khanh linh ơi!

P/s là gì vậy ?