\(A=1+3+3^2+3^3+...+3^{101}\)
\(=>3A=3+3^2+3^3+3^4+...+3^{102}\)
\(=>3A-A=\left(3+3^2+3^3+3^4+...+3^{102}\right)-\left(1+3+3^2+3^3+...+3^{101}\right)\)
\(=>2A=3^{102}-1\)
\(=>A=\dfrac{3^{102}-1}{2}\)

giúp mik nếu đúg mik sẽ tik

giúp mik ik

\(A=1+2+2^2+...+2^{119}\\ =\left(1+2\right)+\left(2^2+2^3\right)+...+\left(2^{118}+2^{119}\right)\\ =\left(1+2\right)+2^2\left(1+2\right)+...+2^{118}\left(1+2\right)\\ =\left(1+2\right)\left(1+2^2+...+2^{118}\right)\\ =3\left(1+2^2+...+2^{118}\right)⋮3\\ \\ A=1+2+2^2+...+2^{119}\\ A=\left(1+2+2^2\right)+...+\left(2^{117}+2^{118}+2^{119}\right)\\ A=\left(1+2+2^2\right)+...+2^{117}\left(1+2+2^2\right)\\ =\left(1+2+2^2\right)\left(1+...+2^{117}\right)\\ =7.\left(1+...+2^{117}\right)⋮7\)

Còn các ý sau bạn tự làm theo cách này tiếp nha!

sao vậy không làm tiếp vậy bạn

\(S=3^1+3^2+3^3+.....+3^{100}\) \(=\left(3^1+3^2+3^3+3^4\right)+\left(3^5+3^6+3^7+3^8\right)+...+\left(3^{97}+3^{98}+3^{99}+3^{100}\right)\)

\(=120+3^5.\left(3^1+3^2+3^3+3^4\right)+....+3^{97}.\left(3^1+3^2+3^3+3^4\right)\)

\(=1.120+3^5.120+...+3^{97}.120\)

\(=\left(1+3^5+...+3^{97}\right).120\)

\(\Rightarrow S⋮120\)

Vậy ........

\(3^{15}+3^{14}+3^{13}\)

\(=3^{13}\left(3^2+3+1\right)=3^{13}\cdot13⋮13\)

\(=3^{13}\left(3^2+3+1\right)=3^{13}\cdot13⋮13\)

Đặt \(A=1+3+3^2+3^3+3^4+\cdot\cdot\cdot+3^{2023}+3^{2024}\)

\(=(1+3+3^2)+(3^3+3^4+3^5)+(3^6+3^7+3^8)+\dots+(3^{2022}+3^{2023}+3^{2024})\\=13+3^3\cdot(1+3+3^2)+3^6\cdot(1+3+3^2)+\dots+3^{2022}\cdot(1+3+3^2)\\=13+3^3\cdot13+3^6\cdot13+\dots+3^{2022}\cdot13\\=13\cdot(1+3^3+3^6+\dots+3^{2022})\)

Vì \(13\cdot(1+3^3+3^6+\dots+3^{2022})\vdots13\)

nên \(A\vdots13\)

\(\Rightarrowđpcm\)

cảm ơn anh nhiều nha!!!!!!

Đề sai rồi bạn

mik gửi nhầm mà

Đề sai rồi bạn

a) 7¹⁰⁴ - 1 = (7⁴)²⁶ - 1 = ...1 - 1 = ...0 \(⋮\)5

b) 3²⁰¹ + 2 = (3⁴)⁵⁰ . 3 + 2 = ...3 + 2 = ...5 \(⋮\)5

A=(4+4^2)+(4^3+4^4)+...+(4^19+4^20)

A=4(1+4)+4^3(1+4)+...+4^19(1+4)

A=(1+4).(4+4^3+...+4^19)

A=5.(4+4^3+..+4^19)

vì 5 chia hết cho =>5.(4+4^3+...+4^19) chí hết cho 5

=> A chia hết cho 5 

câu b làm tương tự cũng nhóm mỗi nhóm là 2 số hạng giống a nha bn

ảnh đại diện là Miku trong Date a live