Question

Ai giúp mk với!!!

Cho D=6+6^2+6^4+...+6^120. Chứng minh D chia hết cho 7, chia hết cho 43

Thanks nha!!!

Answer 1

\(D=6+6^2+6^3+6^4+...+6^{120}\)

\(=\left(6+6^2\right)+\left(6^3+6^4\right)+...+\left(6^{119}+6^{120}\right)\)

\(=6\left(1+6\right)+6^3\left(1+6\right)+...+6^{119}\left(1+6\right)\)

\(=7\left(6+6^3+...+6^{119}\right)\)chia hết cho \(7\).

\(D=6+6^2+6^3+6^4+...+6^{120}\)

\(=\left(6+6^2+6^3\right)+...+\left(6^{118}+6^{119}+6^{120}\right)\)

\(=6\left(1+6+6^2\right)+...+6^{118}\left(1+6+6^2\right)\)

\(=43\left(6+...+6^{118}\right)\)chia hết cho \(43\).

Answer 2

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