Question

Ta có:A=1+2+2²+2³+..........+2¹¹

^{Không tính tổng A hãy chứng minh Achia hết cho 3}

Answer 1

\(A=1+2+...+2^{11}\)

\(=\left(1+2\right)+...+\left(2^{10}+2^{11}\right)\)

\(=1\left(1+2\right)+...+2^{10}\left(1+2\right)\)

\(=1\cdot3+...+2^{10}\cdot3\)

\(=3\cdot\left(1+...+2^{10}\right)⋮3\)

Answer 2

A = 1 + 2 + 2² + ... + 2¹¹

= (1+2) + (2²+2³) + ... + (2¹⁰+2¹¹)

= 3.2²(1+2) + ... + 2¹⁰(1+2)

= 3(2²+...+2¹⁰) \(⋮\)3