Question

Cho A= ( 4ⁿ + 6ⁿ + 8ⁿ +10ⁿ ) - ( 3ⁿ + 5ⁿ + 7ⁿ +9ⁿ ) ( Với n thuộc N). Chứng minh A chia hết cho 2

Answer 1

\(A=\left(4^n+6^n+8^n+10^n\right)-\left(3^n+5^n+7^n+9^n\right)\)

\(A=4^n+6^n+8^n+10^n-3^n-5^n-7^n-9^n\)

\(A=\left(4^n-3^n\right)+\left(6^n-5^n\right)+\left(8^n-7^n\right)+\left(10^n-9^n\right)\)

Vì \(4^n-3^n\)lẻ

      \(6^n-5^n\)lẻ

      \(8^n-7^n\)lẻ 

     \(10^n-9^n\)lẻ

\(\Rightarrow A\)chẵn ( vì lẻ + lẻ +lẻ +lẻ =chẵn ) hay \(A⋮2\)

k cho mình nha !!!!!!!!!!!!!!!

Answer 2

A=(4^n+6^n+8^n+10^n)-(3^n+5^n+7^n+9^n)

A=28^n-24^n

A=4^n

​\(4^n\Rightarrow\)là số chẵn\(\Rightarrow\)Alaf chia hết cho 2