Question

chứng tỏ rằng 5+5 mũ 2 +5 mũ 3 +5 mũ 4 +......5 mũ 29 + 5 mũ 20 chia hết cho 6

Answer 1

Đặt : \(A=5+5^2+5^3+...+5^{30}\)

\(=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{29}+5^{30}\right)\)

\(=5\left(1+5\right)+5^3\left(1+5\right)+...+5^{29}\left(1+5\right)\)

\(=\left(1+5\right)\left(5+5^3+...+5^{29}\right)\)

\(=6\left(5+5^3+...+5^{29}\right)⋮6\) (đpcm)

Answer 2

                                                   Bài giải

\(5+5^2+5^3+5^4+...+5^{29}+5^{30}\)

\(=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{29}+5^{30}\right)\)

\(=5\left(1+5\right)+5^3\left(1+5\right)+...+5^{29}\left(1+5\right)\)

\(=5\cdot6+5^3\cdot6+...+5^{29}\cdot6\)

\(=6\left(5+5^3+...+5^{29}\right)\text{ }⋮\text{ }6\)

\(\Rightarrow\text{ ĐPCM}\)