Ta có : S = 3 + 3² + 3³ + ....+ 3²⁰⁰⁷

\(\Rightarrow S=\left(3+3^2+3^3\right)+....+\left(3^{2005}+2^{2006}+2^{2007}\right)\)

\(\Rightarrow S=3\left(1+3+3^2\right)+.....+3^{2005}\left(1+3+3^2\right)\)

\(\Rightarrow S=3\cdot13+....+3^{2005}\cdot13\)

\(\Rightarrow S=13\cdot\left(3+....+2005\right)\)

\(\Rightarrow S\) chia hết cho 13

đúng nha !!!

a: \(A=2\left(1+2+2^2\right)+...+2^{19}\left(1+2+2^2\right)\)

\(=7\left(2+...+2^{19}\right)⋮7\)

tự làm nha

a: \(A=2\left(1+2+2^2\right)+...+2^{19}\left(1+2+2^2\right)\)

\(=7\left(2+...+2^{19}\right)⋮7\)

a: \(A=2\left(1+2+2^2\right)+...+2^{19}\left(1+2+2^2\right)\)

\(=7\cdot\left(2+...+2^{19}\right)⋮7\)

B = (1 + 3) + (3²+3³)+.....+(3⁸⁹+3⁹⁰)

  = 4 + 3² .(1 + 3) + .....+3⁹⁰.(1+3)

 = 1 .4 + 3².4 + ..... +3⁹⁰.4

= 4.(1 + 3² + .... +3⁹⁰) chia hết cho 4

\(S=3+3^2+3^3+3^4+....+3^{89}+3^{90}\)

\(=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+...+\left(3^{88}+3^{89}+3^{90}\right)\)

\(==3\left(1+3+3^2\right)+3^4\left(1+3+3^2\right)+3^{88}\left(1+3+3^2\right)\)

\(=\left(1+3+3^2\right).\left(3+3^4+....+3^{88}\right)\)

\(=13\left(3+3^4+...+3^{88}\right)\)\(⋮\)\(13\)

SCSH: (3²⁰¹⁵- 1) : 2 = 0

Tổng: (3²⁰¹⁵+ 1) : 2 = 2

Hk tốt,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

k nhé

chưng minh mà anh

S=(1+3+3^2)+(3^3+3^4+3^5)+...+(3^999+3^1000+3^1001)

S=1x(1+3+9)+3^3x(1+3+9)+...+3^999x(1+3+9)

S=1x13+3^3x13+...+3^999x13

S=13x(1+3^3+...+3^999)

Vậy S chia hết cho 13

S=(1+3+3^2)+(3^3+3^4+3^5)+...+(3^999+3^1000+3^1001)

S=1x(1+3+9)+3^3x(1+3+9)+...+3^999x(1+3+9)

S=1x13+3^3x13+...+3^999x13

S=13x(1+3^3+...+3^999)

Vậy S chia hết cho 13

Cảm ơn các bạn nhé . thank you

Có: 3(1+3)+3^3(1+3)+.....+3^59(1+3)

     =3.4+3^3.4+.....+3^59.4

=>S : hết cho 4

Có: 3(1+3+9)+3^4(1+3+9)+.....+3^58(1+3+9)

     =3.13+3^4.13+.....+3^58.13

=>S : hết cho 13

tick cho mình đi !