Question

Chứng minh rằng : A=5 . 5\(^2\) + 5\(^3\) + 5\(^4\) +.........+5\(^{30}\)

      A \(⋮\) 30

Answer 1

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

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

\(\Rightarrow A=\left(5+5^2\right)+5^2\left(5+5^2\right)+...+5^{28}\left(5+5^2\right)\)

\(\Rightarrow A=\left(5+5^2\right)\left(1++5^2+...+5^{28}\right)\)

\(\Rightarrow A=30\left(1++5^2+...+5^{28}\right)⋮30\)