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Đặt \(A=3+3^2+3^3+...+3^{15}\)
\(=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+...+\left(3^{13}+3^{14}+3^{15}\right)\)
\(=3\left(1+3+3^2\right)+3^4\left(1+3+3^2\right)+...+3^{13}\left(1+3+3^2\right)\)
\(=3.13+3^4.13+...+3^{13}.13\)
Vì \(13⋮13\)nên \(3.13+3^4.13+...+3^{13}.13⋮13\)
hay \(A⋮13\)
Vậy \(A⋮13.\)
A=3+3^2+3^3+......+3^13+3^14+3^15
=(3+3^2+3^3)+......+(3^13+3^14+3^15)
=3(1+3+3^2)+.......+3^13(1+3+3^2)
=(3+....+3^13)+(1+3+3^2)
=13(3+.....+3^13) chia hết cho 13
ta có :
\(A=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+\left(3^7+3^8+3^9\right)\)
\(=3.13+3^4.13+3^7.13\)
Vì vậy A chia hết cho 13
A=(3^3+3^4)+(3^5+3^6)+...+(3^15+3^16) = 3^3(1+3)+3^5(1+3) +..+3^15(1+3)= 3^3.4+3^5.4+..+3^15.4 =4.(3^3+3^5+..+3^15)
=> Ạ chia hết cho 4
A=3^3+3^4+3^5+...+3^14+3^15+3^16
A=(3^3+3^4)+(3^5+3^6)+...+(3^15+3^16)
A=3^3(1+3)+3^5(1+3)+...+3^15(1+3)
A=3^3.4+3^5.4+...+3^15.4
A=(3^3+3^5+...+3^15)4
=>A chia hết cho 4
Vậy A=3^3+3^4+3^5+...+3^14+3^15+3^16 chia hết cho 4
a) \(4^{13}+4^{14}+4^{15}+4^{16}=4^{13}\left(1+4\right)+4^{14}\left(1+4\right)=4^{13}.5+4^{14}.5=5\left(4^{13}+4^{14}\right)⋮5\Rightarrow dpcm\)
c) \(2^{10}+2^{11}+2^{12}+2^{13}+2^{14}+2^{15}\)
\(=2^{10}\left(1+2+2^2\right)+2^{13}\left(1+2+2^2\right)\)
\(=2^{10}.7+2^{13}.7=7\left(2^{10}+2^{13}\right)⋮7\Rightarrow dpcm\)
Câu c bạn xem lại đê
ko chia hết.Vì 1+2+3+.......+13 \(⋮\) 1+2+....+13 mà 14 ko\(⋮\) cho 1+2+.......+13
\(A=3+3^2+3^3+...+3^{38}+3^{39}\)
\(=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+...+\left(3^{97}+3^{98}+3^{99}\right)\)
\(=3\left(1+3+9\right)+3^4\left(1+3+9\right)+...+3^{97}\cdot\left(1+3+9\right)\)
\(=13\left(3+3^4+...+3^{97}\right)\)
Vậy \(A⋮13\)
ta có :
A= (3+3^2)+(3^3+3^4)+.......+ (3^15+3^16)
A=3.(3+1)+3^3.(3+1)+.....+3^15.(3+1)
A= 3.4+3^3.4+......+3^15.4
A=4.(3+3^3+.....+3^15) chia hết cho 4
vậy a chia hết cho 4
b. Ta có :
A= (3+3^2+3^3)+......+(3^14+3^15+3^16)
A=3.(1+3+3^2)+.....+3^14.(1+3+3^2)
A=3.13+.....+3^14.13 chia hết cho 13
Vậy A chia hết cho 13
A=3+3^2+3^3+....+3^13+3^14+3^15
=(3+3^2+3^3)+...+(3^13+3^14+3^15)
=3(1+3+3^2)+...+3^13(1+3+3^2)
=(1+3+3^2)(3+...+3^13)
=13(3+...+3^13) chia hết cho 13