Question

[Đoàn Khắc Long]

A=6² + 6³ + 6⁴ + 6⁵ +6⁶ + 6⁷ 

Chứng minh tổng A chia hết cho 42

Answer 1

[Huỳnh Phước Mạnh]

\(A=\left(6^2+6^3\right)+\left(6^4+6^5\right)+\left(6^6+6^7\right)\)

\(A=6\cdot\left(6+6^2\right)+6^3\cdot\left(6+6^2\right)+6^5\cdot\left(6+6^2\right)\)

\(A=6\cdot42+6^3\cdot42+6^5\cdot42\)

\(A=42\cdot\left(6+6^3+6^5\right)⋮42\)(điều phải chứng minh)

Answer 2

[KWS]

\(A=6^2+6^3+6^4+6^5+6^6+6^7\)

\(=\left(6^2+6^3\right)+\left(6^4+6^5\right)+\left(6^6+6^7\right)\)

\(=6\left(6+6^2\right)+6^3\left(6+6^2\right)+6^5\left(6+6^2\right)\)

\(=6.42+6^3.42+6^5.42\)

\(=42\left(6+6^3+6^5\right)⋮42\left(đpcm\right)\)