\(S=1-2+2^2-2^3+...+2^{2012}-2^{2013}\)

\(\Rightarrow2S=2-2^2+2^3-2^4+...+2^{2013}-2^{2014}\)

\(\Rightarrow2S+S=2-2^2+2^3-...-2^{2014}+1-2^2-2^3+...-2^{2013}\)

\(\Rightarrow3S=1-2^{2014}\)\(\Rightarrow3S-2^{2014}=1-2^{2015}\)

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

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

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

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

\(\Rightarrow dpcm\)

ta có: \(S=1-2+2^2-2^3+2^4-2^5+...+2^{2013}-2^{2014}\)

\(\Rightarrow2S=2-2^2+2^3-2^4+2^5-2^6+...+2^{2014}-2^{2015}\)

=> 2S + S = -2²⁰¹⁵ + 1

=> 3S = -2²⁰¹⁵ + 1

=> 3S - 1 = -2²⁰¹⁵

=> 1 - 3S = 2²⁰¹⁵

( cn về S = 1 - 2 + 22 - 23 + 24-25+...+22013 - 22014 mk vx chưa hiểu quy luật của nó lắm, thật lòng xl bn nha! mk chỉ bk z thoy!)

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

S=(1+2)+...+2^6(1+2)=3(1+...+2^6)⋮3

S = (1+ 2)+(22 + 23 )+( 24 + 27) + (26 + 25)

S=   3+45+51+51

S=3+3.15+3.17+3.17

S=3.(1+15+17.2): hết 3

tick nha nhanh nhất nè

vì tổng của S chia hết cho 3 nên S chia hết cho 3. có thế cũng hỏi =))

Chúc bạn an toàn

ta thấy : 1/21>1/33;...1/30>1/33

Vậy 1/21+..+1/30>1/33+...+1/33(10 lần 1/33)

1/3=11/33

mà 1/33+..+1/33(10 lần 1/33) =10/33

Suy ra S>1/33+..+1/33(10 lần 1/33)>1/3

Vậy S>1/3

nhớ k nha bạn 

viết lôn nha câu đầu la .. 1/30.>1/33

Thanks

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

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

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

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

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