\(S=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{95}+2^{96}\right)\\ S=\left(1+2\right)\left(2+2^3+...+2^{95}\right)\\ S=3\left(2+2^3+...+2^{95}\right)⋮3\left(1\right)\\ S=\left(2+2^2\right)+2^3\left(1+2^2+...+2^{93}\right)\\ S=8+8\left(1+2^2+...+2^{93}\right)⋮8\left(2\right)\\ \left(1\right)\left(2\right)\Rightarrow S⋮24\)

\(S=1+2+2^2+2^3+2^4+...+2^{2011}\)

\(\Rightarrow S=\left(1+2+2^2\right)+2^3\left(1+2+2^2\right)+...+2^{2009}\left(1+2+2^2\right)\)

\(\Rightarrow S=7+2^3.7+...+2^{2009}.7\)

\(\Rightarrow S=7\left(1+2^3+...+2^{2009}\right)⋮7\)

\(\Rightarrow dpcm\)

a) S=(2+2²)+2²(2+2²)+2⁴(2+2²)+.....+2⁹⁸(2+2²)

S=(2+2²)(1+2²+2⁴+....+2⁹⁸)

s=6(1+2²+2⁴+....+2⁹⁸)

Vi 6 chia het cho 3.Suyra S chia het cho 3

Moi cac ban xem tiep phan sau vao ngay mai

a. S=2+2^2+2^3+2^4+...+2^100

= 2.(1+2)+2^3.(1+2)+2^5.(1+2)+....+2^99(1+2)

=2.3+2^3.3+2^5.3+...+2^99.3

=3.(2+2^2+2^5+...+2^99)

=> 3 chia hết cho 3 

b. S=2+2^2+2^3+2^4+...+2^100

= 2.(1+2+4+8)+2^5.(1+2+4+8)+2^9(1+2+4+8)+...+2^96.(1+2+4+8)

=2.15+2^5.15+2^9.15+...+2^96.15

=> S chia hết cho 15 

a) S = ( 2 + 2^2 ) + ( 2^3 + 2^4 ) + ... + ( 2^99 + 2^100 )

S = 2(1 + 2 ) + 2^3(1 + 2 ) + ... + 2^99( 1 + 2 )

S = 2 . 3 + 2^3 . 3 + ... + 2^99 . 3

S = 3( 2 + 2^3 + 2^99 ) chia hết cho 3

ý b, c làm tương tự

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

\(S=1+2+2^2+2^3+...+2^{59}\)

\(S=\left(1+2\right)+\left(2^2+2^3\right)+...+\left(2^{58}+2^{59}\right)\)

\(S=3+2^2\cdot3+...+2^{58}\cdot3\)

\(S=3\cdot\left(1+2^2+...+2^{58}\right)\)

S chia hết cho 3

_____

\(S=1+2+2^2+...+2^{59}\)

\(S=\left(1+2+2^2\right)+\left(2^3+2^4+2^5\right)+...+\left(2^{57}+2^{58}+2^{59}\right)\)

\(S=7+7\cdot2^3+...+7\cdot2^{57}\)

\(S=7\cdot\left(1+2^3+...+2^{57}\right)\)

S chia hết cho 7 

_____

\(S=1+2+2^2+2^3+...+2^{59}\)

\(S=\left(1+2+2^2+2^3\right)+\left(2^4+2^5+2^6+2^7\right)+...+\left(2^{56}+2^{57}+2^{58}+2^{59}\right)\)

\(S=15+2^4\cdot15+...+2^{56}\cdot15\)

\(S=15\cdot\left(1+2^4+...+2^{56}\right)\)

S chia hết cho 15 

\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{99}+2^{100}\right)\\ A=\left(2+2^2\right)+2^2\left(2+2^2\right)+...+2^{98}\left(2+2^2\right)\\ A=\left(2+2^2\right)\left(1+2^2+...+2^{98}\right)\\ A=6\left(1+2^2+...+2^{98}\right)⋮6\)