Question

cho A = 5+5²⁺5³+.....+5²⁰

^{chúng minh A chia hết cho 3}

Answer 1

Ta có:
\(A=5+5^2+5^3+...+5^{20}\)
\(=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{19}+5^{20}\right)\)
\(=30+\left(5+5^2\right).\left(5^2+5^2\right)+...+\left(5+5^2\right).\left(5^{18}+5^{18}\right)\)
\(=30+30.\left(5^2+5^2\right)+...+30.\left(5^{18}+5^{18}\right)\)
\(=30.\left(1+5^2+5^2+...+5^{18}+5^{18}\right)⋮30\)
Mà \(30⋮3\)
\(\Rightarrow A⋮3\)

Answer 2

5A=5^2+5^3+5^4+....5^21

5A-A=(5^2+5^3+5^4+....5^21)-(5+5^2+...+5^20)

4a=5^21-5

A=(5^21-5)/4