Toán A=(2n-1)(2n+3) – (4n-5)(n+1)+3 CMR A chia hết cho 5 28/07/2021 By Melody A=(2n-1)(2n+3) – (4n-5)(n+1)+3 CMR A chia hết cho 5
`A=(2n-1)(2n+3) – (4n-5)(n+1)+3` `A=4n^2+6n-2n-3-4n^2-4n+5n+5+3` `A=5n+5` `A=5(n+5)` chia hết cho `5 ∀x` Vậy `A` chia hết cho `5` Trả lời
\(A=(2n-1)(2n+3)-(4n-5)(n+1)+3\) \(=4n^2+6n-2n-3-4n^2-4n+5n+5+3\) \(=(4n^2-4n^2)+(6n-2n-4n+5n)+(5+3-3)\) \(=5n+5\) \(=5(n+1)\forall n\) Vậy \(A\vdots5\) Trả lời
`A=(2n-1)(2n+3) – (4n-5)(n+1)+3`
`A=4n^2+6n-2n-3-4n^2-4n+5n+5+3`
`A=5n+5`
`A=5(n+5)` chia hết cho `5 ∀x`
Vậy `A` chia hết cho `5`
\(A=(2n-1)(2n+3)-(4n-5)(n+1)+3\)
\(=4n^2+6n-2n-3-4n^2-4n+5n+5+3\)
\(=(4n^2-4n^2)+(6n-2n-4n+5n)+(5+3-3)\)
\(=5n+5\)
\(=5(n+1)\forall n\)
Vậy \(A\vdots5\)