\(A=2+2^2+2^3+2^4+...+2^{59}+2^{60}\)

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

\(=3.\left(2+2^3+...+2^{59}\right)\) ⋮ 3

con khong biet

Sai hết :)

cứu

gấp 

\(a,2A=2+2^2+2^3+...+2^{100}\\ \Rightarrow2A-A=2+2^2+...+2^{100}-1-2-...-2^{99}\\ \Rightarrow A=2^{100}-1\\ b,A=\left(1+2\right)+2^2\left(1+2\right)+...+2^{98}\left(1+2\right)\\ A=\left(1+2\right)\left(1+2^2+...+2^{98}\right)=3\left(1+2^2+...+2^{98}\right)⋮3\\ c,A=\left(1+2+2^2+2^3\right)+...+2^{96}\left(1+2+2^2+2^3\right)\\ A=\left(1+2+2^2+2^3\right)\left(1+...+2^{96}\right)=15\left(1+...+2^{96}\right)⋮15\)

ta có :

A = 3 + 3² + 3³ + ...+ 3⁵⁹ + 3⁶⁰  

A = ( 3 + 3² + 3³ ) + ( 3⁴ + 3⁵ + 3⁶ ) + ...+ ( 3⁵⁸ + 3⁵⁹ + 3⁶⁰ )

A = 3( 1 + 3 + 3²) + 3⁴(1+3+3²) + ...+ 3⁵⁸(1+3+3² )

A = 3. 13 + 3⁴.13 + ...+ 3⁵⁸.13 

=> A chia hết cho 13 

Ta chú ý : \(3+3^2+3^3=3\left(1+3+9\right)=3.13\)

\(\Rightarrow A=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+..+\left(3^{58}+3^{59}+3^{60}\right)\)

\(\Leftrightarrow A=3.13+3^4.13+...+3^{58}.13\)

\(\Leftrightarrow A=13\left(3+3^4+..+3^{58}\right)⋮13\)

Vậy A chia hết cho 13

3mũ2

Tôi  tên  là  Ngọc  Anh  . Năm  nay  Tôi 11 tuổi.  Tôi  không  biết  bài  này  

câu a của bạn thiếu 2 mũ 2

67aiijajjhq

d

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