Cho S = 1+2+2^2+2^3+2^4+2^5+2^6+2^7
Chứng tỏ rằng S chia hết cho 3
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(S=1+2+2^2+2^3+2^4+2^5+2^6+2^7\)
\(\Rightarrow S=\left(1+2\right)+\left(2^2+2^3\right)+\left(2^4+2^5\right)+\left(2^6+2^7\right)\)
\(\Rightarrow S=\left(1+2\right)+2^2\left(1+2\right)+2^4\left(1+2\right)+2^6\left(1+2\right)\)
\(\Rightarrow S=\left(1+2\right)\left(1+2^2+2^4+2^6\right)\)
\(\Rightarrow S=3\left(1+2^2+2^4+2^6\right)⋮3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 3:
\(A=5+5^2+..+5^{12}\)
\(5A=5\cdot\left(5+5^2+..5^{12}\right)\)
\(5A=5^2+5^3+...+5^{13}\)
\(5A-A=\left(5^2+5^3+...+5^{13}\right)-\left(5+5^2+...+5^{12}\right)\)
\(4A=5^2+5^3+...+5^{13}-5-5^2-...-5^{12}\)
\(4A=5^{13}-5\)
\(A=\dfrac{5^{13}-5}{4}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
S=(1+2)+(22+23)+.....+(26+27)
S= 3 +22(1+2)+....+26(1+2)
S= 3 +22.3+.....+26.3
S= 3(1+22+.....+26)chia hết cho 3
Tick mình đầu tiên nha
![](https://rs.olm.vn/images/avt/0.png?1311)
Chọn mình nhé:
1+2+22+23+24+25+26+27
=(1+2)+(22+23)+(24+25)+(26+27)
=3+2(1+2)+...+26(1+2)
=3+2.3+...+26.3
Ta thấy mỗi thừa số đều chia hết cho 3 nên S chia hết cho 3
![](https://rs.olm.vn/images/avt/0.png?1311)
S = 1 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7
S = (1+2) + (2^2 + 2^3) + (2^4 + 2^5) + (2^6 + 2^7)
S = (1+2) + 2^2 (1+2) + 2^4 (1+2) + 2^6 (1+2)
S = 3*1 + 2^2 * 3 + 2^4 * 3 + 2^6 * 3
S = 3 * (1 + 2^2 + 2^4 + 2^6)
Vì 3 ⁝ 3
nên 3 * (1 + 2^2 + 2^4 + 2^6) ⁝ 3
Vậy S ⁝ 3
S = 1 + 2 + 22 + 23 + 24 + 25 + 26 + 27
S = (1 + 2) + (22 + 23) + (24 + 25) + (26 + 27)
S = 1(1 + 2) + 22(1 + 2) + 24(1 + 2) + 26(1 + 2)
S = (1 . 3) + (22 . 3) + (24 . 3) + (26 . 3)
S = 3 . (1 + 22 + 24 + 26) ⋮ 3
S ⋮ 3
![](https://rs.olm.vn/images/avt/0.png?1311)
\(S=\left(1+2+2^2\right)+\left(2^3+2^4+2^5\right)+...+\left(2^{15}+2^{16}+2^{17}\right)\)
\(S=7+2^3\left(1+2+2^2\right)+...+2^{15}\left(1+2+2^2\right)\)
\(S=7\left(1+2^3+...+2^{15}\right)\) chia hết cho 7
![](https://rs.olm.vn/images/avt/0.png?1311)
S = 1 + 2 + 22 + 23 + 24 + 25 + 26 + 27
S = ( 1 + 2 ) + ( 22 + 23 ) + ( 24 + 25 ) + ( 26 + 27 )
S = 3 + 22 . ( 1 + 2 ) + 24 . ( 1 + 2 ) + 26 . ( 1 + 2 )
S = 3 + 22 . 3 + 24 . 3 + 26 . 3
S = 3 . ( 1 + 22 + 26 ) chia hết cho 3
![](https://rs.olm.vn/images/avt/0.png?1311)
S = (1 + 2) + (2^2 + 2^3) + (2^4 + 2^5) + (2^6 + 2^7)
S= 1.1 + 2.1 + 2^2.1+2^2.2+ 2^4.1+2^4.2 + 2^6.1 + 2^6.2
S = 1.(1+2) + 2^2.(1+2) + 2^4.(1+2) + 2^6.(1 + 2)
S = 1.3 + 2^2.3 + 2^4.3 +2^6.3
S = 3.(1+2^2+2^4+2^6)
S chia hết cho 3
cái lòn con gái banh ra , con kẹt con trai thụt vào rồi liếm vào đó...........( tự hiểu, phê chưa)