Question

Tập hợp các số tự nhiên thỏa mãn là ...

Answer 1

n+5 ⋮ n+1

=> n+1+4 ⋮ n+1

Vì n+1 ⋮ n+1 nên để n+1+4 ⋮ n+1 thì 4 ⋮ n+1

=> n+1 \(\in\) Ư(4) = {1;2;4}

n+1	1	2	4
n	0	1	3

Vậy n = {0;1;3}

Answer 2

Ta có : \(n+5⋮n+1\) ; Mà : \(n+1⋮n+1\)

\(\Rightarrow\left(n+5\right)-\left(n+1\right)⋮n+1\Rightarrow n+5-n-1⋮n+1\)

\(\Rightarrow4⋮n+1\Rightarrow n+1\inƯ\left(4\right)\)

Mà : \(Ư\left(4\right)=\left\{1;2;4\right\}\) ; \(n+1\ge1\Rightarrow n+1\in\left\{1;2;4\right\}\Rightarrow n\in\left\{0;1;3\right\}\)

Vậy ...

Answer 3

n+5 chia cho n+1

ta co : n+5=n+1+5

vi n+1 chia het cho n+1 de n+1+4 chia het cho n+1

thi 4 chia het cho n+1 thuoc u(4)

ma u(4)={-4;-2;-1;1;2;4}

ta co n+1=-4

n =--5

n+1=-2

n =-1

n+1=-1

n =-2

n+1=1

n =0

n+1=2

n =1

n+1=4

n =3

vi de bai cho n la so tu nhien nen ta chon n=0 hoac n=1 hoac n=3

vay n=0 hoac n= 1 hoac n=3 thi 2chia het cho n+1

 

Answer 4

n+5\(⋮\)n+1

(n+1)+4\(⋮\)n+1

Vì n+1\(⋮\)n+1

Buộc 4\(⋮\)n+1=>n+1ϵƯ(4)={1;2;4}
Với n+1=1=>n=0

n+1=2=>n=1

n+1=4=>n=3

Vậy nϵ{0;1;3}