Question

P/S:bai nay khong lien quan den uoc va boi

2 mũ 1 +...+2 mũ 10 co chia het cho 3 khong

may ban than dong giup minh voi

Answer 1

2¹+2²+2³+......+2¹⁰

⇒2.(1+2)+2².(1+2)+......+2⁹.(1+2)

⇒2.3+2².3+........+2⁹.3

⇒3.(2+2²+....+2⁹)⋮3

Vậy 2¹+2²+2³+....+2¹⁰⋮3 (đpcm)

Answer 2

Đặt biểu thức trên là A, ta có:

\(A=2^1+2^2+2^3+...+2^{10}\)

\(A=\left(2^1+2^2\right)+\left(2^3+2^4\right)+...+\left(2^9+2^{10}\right)\)

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

\(A=2^1.3+2^3.3+...+2^9.3\)

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

\(\Rightarrow A⋮3\)

Answer 3

2¹+2²+2³+....+2¹⁰

=2.(1+2)+2².(1+2)+........+2⁹.(1+2)

=2.3+2².3+...+2⁹.3

=3.(2+2²+....+2⁹)

vi 3⋮3=>3.(2+2²+....+2⁹)

vậy 2+2²+2³+...+2¹⁰ ⋮ 3