Question

tổng sau có chia hết cho 3 ko?

A=2+2 mũ 2+ 2 mũ 3+ 2 mũ 4+2 mũ 5+......+2 mũ 9+2 mũ 10

 

Answer 1

A = 2 + 2² + 2³ + 2⁴ + ... + 2⁹ + 2¹⁰ (có 10 số; 10 chia hết cho 2)

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 2

suy ra 2A=2^2 + 2^3 +2^4 +... +2^10+2^11

=>2A-A=2^2 +2^3+...+2^11-2-2^2-2^3-...-2^10=2^11-2=2046

Answer 3

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

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

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

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

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

\(\Rightarrow\)\(A\)chia hết cho \(3\)

Answer 4

de ma ban