\(S=1+2+2^2+2^3+...+2^{99}\)

   \(=\left(1+2+2^2+2^3\right)+...+\left(2^{96}+2^{97}+2^{98}+2^{99}\right)\)

   \(=\left(1+2+4+8\right)+...+2^{96}.\left(1+2+2^2+2^3\right)\)

   \(=15+...+2^{96}.15\)

   \(=15.\left(1+...+2^{96}\right)⋮15\)

\(\Rightarrow\) \(S⋮15\)

sai đề , ai thấy sai đề tick mk nha

\(A=3^1+3^2+...+3^{30}\)

=> A=3(1+3) +...+ 3²⁹(1+3)

        =3.4+ ... + 3²⁹.4 \(⋮\)4

Chia het 13 ban lam tuong tu nhe

\(1;a,942^{60}-351^{37}\)

\(=\left(942^4\right)^{15}-\left(....1\right)\)

\(=\left(....6\right)^{15}-\left(...1\right)\)

\(=\left(...6\right)-\left(...1\right)=\left(....5\right)⋮5\)

\(b,99^5-98^4+97^3-96^2\)

\(=\left(...9\right)-\left(...6\right)+\left(...3\right)-\left(...6\right)\)

\(=\left(...6\right)-\left(...6\right)=\left(...0\right)⋮2;5\)

\(2;5n-n=4n⋮4\)

chả hiểu j

\(Tacó:\hept{\begin{cases}2a+5⋮7\\7a+7⋮7\end{cases}}\Rightarrow\hept{\begin{cases}5a+2⋮7\\7⋮7\end{cases}}\Rightarrow\hept{\begin{cases}10a+4⋮7\\7⋮7\end{cases}}\)

\(\Rightarrow10a+4+7=10a+11⋮7\left(dpcm\right)\)

b, tự tương

\(a,2a+5⋮7\Leftrightarrow2a+5+28a+28⋮7\)         (  vì \(28a+28⋮7\) ) 

                     \(\Leftrightarrow30a+33⋮7\)

                     \(\Leftrightarrow3.\left(10a+11\right)⋮7\)

                     \(\Leftrightarrow10a+11⋮7\)   (  vì \(\left(3;7\right)=1\) ) 

Vậy \(2a+5⋮7\Leftrightarrow10a+11⋮7\)

Câu b bn xem lại đề hộ mk chút nhé!

a) S = 3 + 32 + ... + 31998

=> S = ( 3 + 3² ) + ... + ( 3¹⁹⁹⁷ + 3¹⁹⁹⁸ )

=> S = ( 3 + 9 ) + ... + 3¹⁹⁹⁶ . ( 3 + 3² )

=> S = 12 + ... + 3¹⁹⁹⁶ . 12

=> S = ( 1 + ... + 3¹⁹⁹⁶ ) . 12 chia hết cho 12

=> S chia hết cho 12

b) S = 3 + 3² + ... + 3¹⁹⁹⁸

=> S = ( 3 + 3² + 3³ ) + ... + ( 3¹⁹⁹⁶ + 3¹⁹⁹⁷ + 3¹⁹⁹⁸ )

=> S = 39 + ... + 3¹⁹⁹⁵ . ( 3 + 32 + 33 )

=> S = 39 + ... + 3¹⁹⁹⁵ . 39

=> S = ( 1 + ... + 3¹⁹⁹⁵ ) . 39 chia hết cho 39

=> S chia hết cho 39