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 \(S⋮3\left(đpcm\right)\)

S = 1 + 2 + 2² + 2³ +...+2⁷ ( có 8 số hạng)

S = (1+2) + (2² + 2³) + ...+ (2⁶ +2⁷)

S = 3 + 2².(1+2) + ...+ 2⁶.(1+2)

S = 3.(1+2²+...+2⁶) chia hết cho 3

\(S=1+2+2^2+2^3+2^4+2^5+2^6+2^7\)

\(\Rightarrow S=\left(1+2\right)+\left(2^2+2^3\right)+\left(2^4+2^5\right)+\left(2^6+2^7\right)\)

\(\Rightarrow S=\left(1+2\right)+2^2\left(1+2\right)+2^4\left(1+2\right)+2^6\left(1+2\right)\)

\(\Rightarrow S=\left(1+2\right)\left(1+2^2+2^4+2^6\right)\)

\(\Rightarrow S=3\left(1+2^2+2^4+2^6\right)⋮3\)

S=(1+2)+...+2^6(1+2)=3(1+...+2^6)⋮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

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 

đg định làm thì đã có người xong rồi
 

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) chia hết cho 3

cái lòn con gái banh ra , con kẹt con trai thụt vào rồi liếm vào đó...........( tự hiểu, phê chưa)

Bài 3:

\(A=5+5^2+..+5^{12}\)

\(5A=5\cdot\left(5+5^2+..5^{12}\right)\)

\(5A=5^2+5^3+...+5^{13}\)

\(5A-A=\left(5^2+5^3+...+5^{13}\right)-\left(5+5^2+...+5^{12}\right)\)

\(4A=5^2+5^3+...+5^{13}-5-5^2-...-5^{12}\)

\(4A=5^{13}-5\)

\(A=\dfrac{5^{13}-5}{4}\)

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

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 + 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