tổng của ba số tự nhiên có chia hết cho ba hay không ? tổng của bốn số tự nhiên liên tiếp có chia hết cho bốn hay không ?
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a) gọi 3 số tự nhiên liên tiếp là a ; a+1 ; a+2 ( a thuộc N )
ta có : a+(a+1)+(a+2)=3a+3=3 . ( a + 1 ) chia hết cho 3
vậy tổng của 3 số liên tiếp chia hết cho 3
b) gọi 4 số tự nhiên liên tiếp là a ; a+1 ; a+2 ; a+3 ( a thuộc N )
ta có : a+(a+1)+(a+2)+(a+3)=4a + 6 không chia hết cho 4 ( 6 không chia hết cho 4 )
A, CÓ
B,KHÔNG
C,GOI BA SO TU NHIEN LIEN TIEP LA A,A+1, A+2,
(a+a+a)+ (1+2)
3a+3 chia hết cho 3
vi 3chia hết cho 3
vậy tổng 3 số tự nhiên liên tiếp chia hết cho 3
gọi 4 số tự nhiên liên tiếp là a,á+1,a+2,a+3
(a+a+a+a)+(1+2+3)
4a+6 không chia hết cho 3 vì 4 không chia hết cho 3
vậy tổng 4 số tự nhiên liên tiếp không chia hết cho 3
a) Gọi ba số tự nhiên liên tiếp là a,a+1,a+2
Có tổng của ba số tự nhiên liêp tiếp là
a+a+1+a+2=a+a+a+1+2=a.3+3 chia hết cho 3
b)Gọi 4 số tự nhiên liên tiếp là a,a+1,a+2,a+3
Có tổng của ba số tự nhiên liêp tiếp là
a+a+1+a+2+a+3=a.4+6 ko chia hết cho 4
a,
Gọi hai số tự nhiên liên tiếp là a và a + 1
Nếu a chia hết cho 2 thì bài toán được chứng minh.
Nếu a không chia hết cho 2 thì a = 2k + 1 (k∈N)
Suy ra: a + 1 = 2k + 1 + 1 = 2k + 2
Ta có: 2k ⋮ 2; 2 ⋮ 2
Suy ra: (2k + 2) ⋮ 2 hay (a + 1) ⋮ 2
Vậy trong hai số tự nhiên liên tiếp, có một số chia hết cho 2
Mik chỉ làm được câu a thôi nhưng vẫn mong bạn ủng hộ ^-^
a) hai số liên tiếp thì sẽ có 1 số chẵn và 1 số lẻ , số chẵn là số chia hết cho 2 nên trong hai số tự nhiên liên tiếp sẽ có 1 số chia hết cho 2
a) Vì có 1 số chẵn và 1 số lẻ trong 2 số tự nhiên liên tiếp nên chia hết cho 2
b) Trong 3 số tự nhiên liên tiếp thì có số cộng các chữ số của số đó chia hết cho3
c) Tổng 2 số tự nhiên liên tiếp là chẵn + lẻ = lẻ nên ko chia hết cho 2
d) 3 số tự nhiên liên tiếp thì có 1 số chia 3 dư 1 , 1 số chia 3 dư 2 , 1 số chia hết cho 3 nên lấy số dư là 1+2=3 chia hết cho 3 nên tổng 3 số tự nhiên liên tiếp chia hết cho 3
a, Gọi 3 số tự nhiên liên tiếp là n; n+1 và n+2
Tổng chúng: n+(n+1)+(n+2)= 3n+3\(⋮\) 3 \(\forall n\in N\) (đpcm)
b, Gọi 4 số tự nhiên liên tiếp là n; n+1; n+2; n+3
Tổng chúng: \(n+\left(n+1\right)+\left(n+2\right)+\left(n+3\right)=4n+6⋮̸4\forall n\in N\left(Vì:4n⋮4;6⋮̸4\right)\left(đpcm\right)\)
c, Hai số tự nhiên liên tiếp là k và k+1
Tích chúng: k(k+1) . Nếu k chẵn thì k+1 lẻ => Tích chẵn, chia hết cho 2
Nếu k lẻ thì k+1 chẵn => Tích chẵn, chia hết cho 2
(ĐPCM)
d, Ba số tự nhiên liên tiếp là m;m+1 và m+2
Tích chúng: m(m+1)(m+2)
+) TH1: Nếu m chia hết cho 3 => Tích 3 số chia hết cho 3
+) TH2: Nếu m chia 3 dư 1 => m+2 chia hết cho 3 => Tích 3 số chia hết cho 3
+) TH3: Nếu m chia 3 dư 2 => m+1 chia hết cho 3 => Tích 3 số chia hết cho 3
=> Kết luận: Tích 3 số tự nhiên liên tiếp chia hết cho 3 (đpcm)
?
Kham khảo nhé:
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)