Question

Tổng sau có chia hết cho 3 không ?

\(A=2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^{10}\)

Answer 1

\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^9+2^{10}\right)\)

\(A=2.\left(1+2\right)+2^3.\left(1+2\right)+...+2^9.\left(1+2\right)\)

\(A=2.3+2^3.3+...+2^9.3\)

\(A=3.\left(2+2^3+...+2^9\right)⋮3\)

Answer 2

A = 2 + 2² +...+ 2¹⁰ ( có 10 số hạng)

A = (2+2² ) +( 2³+2⁴) + ...+ (2⁹+2¹⁰) 

A = 2.(1+2) + 2³.(1+2) + ...+ 2⁹.(1+2)

 A = 2.3 + 2³.3 + ...+ 2⁹.3

A = 3.(2+2³ +...+2⁹) chia hết cho 3

Answer 3

Tổng này CÓ CHIA HẾT CHO 3

Answer 4

A = 2+2² +...+2¹⁰ ( có 10 số hạng )

A = (2+2²) + (2³ +2⁴ )+...+(2⁹ +2¹⁰ )

A = 2.(1+2)+2³.(1+2)+...+2⁹.(1+2)

A = 2.3 + 2³.3 +...+ 2⁹.3

A = 3. (2+2³+...+2⁹) chia hết cho 3

Answer 5

\(A=2+2^2+2^3+2^4+....+2^9+2^{10}\)

\(=\left(2+2^2\right)+\left(2^3+2^4\right)+....+\left(2^9+2^{10}\right)\)

\(=\left[2\left(1+2\right)\right]+\left[2^3\left(1+2\right)\right]+....+\left[2^9\left(1+2\right)\right]\)

\(=2\cdot3+2^3\cdot3+.....+2^9\cdot3\)

\(=3\left(2+2^3+....+2^9\right)\)

\(\Rightarrow A⋮3\)