Question

Chứng minh: A = 2¹ + 2² + 2³ + 2⁴ + ... + 2²⁰¹⁰ chia cho 3 và 7.

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Answer 1

*)\(A=2+2^2+2^3+2^4+...+2^{2010}\)

\(\Rightarrow A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{2009}+2^{2010}\right)\)

\(\Rightarrow A=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{2009}\left(1+2\right)\)

\(\Rightarrow A=2\cdot3+2^3\cdot3+...+2^{2009}\cdot3\)

\(\Rightarrow A=3\cdot\left(2+2^3+...+2^{2009}\right)\)

\(\Rightarrow A⋮3\)

*)\(A=2+2^2+2^3+...+2^{2010}\)

\(\Rightarrow A=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{2008}+2^{2009}+262010\right)\)

\(\Rightarrow A=2\cdot\left(1+2+2^2\right)+2^4\cdot\left(1+2+2^2\right)+...+2^{2008}\left(1+2+2^2\right)\)

\(\Rightarrow A=2\cdot7+2^4\cdot7+...+2^{2008}\cdot7\)

\(\Rightarrow A=7\cdot\left(2+2^4+...+2^{2008}\right)\)

\(\Rightarrow A⋮7\)

Answer 2

Thiếu đề. A chia cho 3 và 7 rồi sao nữa

Answer 3

cung chia het cho a

Answer 4

Đâu có thiếu đâu đúng mà.

Answer 5

\(A=2^1+2^2+2^3+....+2^{2010}\)

\(=2\left(1+2\right)+2^3\left(1+2\right)+2^5\left(1+2\right)+....+2^{2009}\left(1+2\right)\)

\(=3\left(2+2^3+2^5+....+2^{2009}\right)\)\(⋮3\)

\(A=2^1+2^2+2^3+...+2^{2010}\)

\(=2\left(1+2+2^2\right)+2^4\left(1+2+2^2\right)+....+2^{2008}\left(1+2+2^2\right)\)

\(=7\left(2+2^4+2^7+...+2^{2008}\right)\) \(⋮7\)

Answer 6

A= (2^1+2^2+2^3)+(2^4+2^5+2^6)+......+(2^2008+2^2009+2^2010)

A=2(1+2+2^2)+2^4(1+2+2^2)+.....+2^2008(1+2+2^2)

A=2*7+2^4*7+......+2^2008*7  chia hết cho 7

Answer 7

A=(2+2^2)+(2^3+2^4)+............+(2^2009+2^2010)

A=2(1+2)+2^3(1+2)+....+2^2009(1+2)

A=2*3+2^3*3+.....+2^2009*3 chia hết cho 3