S=1+2+2^2+2^3+2^4+2^5+2^6+2^7.Chứng tỏ S chia hết cho 3
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\(S=1+2+2^2+2^3+2^4+2^5+2^6+2^7\)
\(\Rightarrow S=\left(1+2\right)+\left(2^2+2^3\right)+\left(2^4+2^5\right)+\left(2^6+2^7\right)\)
\(\Rightarrow S=\left(1+2\right)+2^2\left(1+2\right)+2^4\left(1+2\right)+2^6\left(1+2\right)\)
\(\Rightarrow S=\left(1+2\right)\left(1+2^2+2^4+2^6\right)\)
\(\Rightarrow S=3\left(1+2^2+2^4+2^6\right)⋮3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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
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cái lòn con gái banh ra , con kẹt con trai thụt vào rồi liếm vào đó...........( tự hiểu, phê chưa)
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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 = 3 + 2^2 . ( 1 + 2 ) + 2^4 . ( 1 + 2 ) + 2^6 . ( 1 + 2 )
S = 3 + 2^2 . 3 + 2^4 . 3 + 2^6 . 3
S = 3 . ( 2^2 + 2^4 + 2^6 )
Vi 3 chia het cho 3 nen 3 . ( 2^2 + 2^4 + 2^6 ) chia het cho 3
hay S chia het cho 3
\(S=1+2+2^2+2^3+2^4+2^5+2^6+2^7\)
\(\Rightarrow S=\)\(S=(1+2)+(2^2+2^3)+(2^4+2^5)+(2^6+2^7)\)
\(\Rightarrow S=\left(1+2\right)+2^2\left(1+2\right)+2^4\left(1+2\right)+2^6\left(1+2\right)\)
\(\Rightarrow S=3\cdot\left(1+2^2+2^4+2^6\right)⋮3\)
VẬY \(S⋮3\left(đpcm\right)\)
![](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
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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(22+24+26+1)
=> S chia hết 3
k tui nha. Tui là ARMY nè. Bias của tui là Chây Hốp
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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
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