Question

Chứng minh rằng: A=5+5²+5³+...+5⁸ là B (30)

Answer 1

A = 5 + 5^2 + 5^3 +...+5^8 

A = ( 5 + 5^2 ) + ( 5^3 + 5^4) +...+(5^7+5^8)

A = 30 +5(5+5^2) +...+ 5^6(5 + 5^2)

A=30 + 5 . 30 +...+5^6 .30

A = 30( 1 + 5 + ...+ 5^ 6) chia hết cho 30 

A chia hết cho 30

Answer 2

\(A=5+5^2+5^3+5^4+5^5+5^6+5^7+5^8\)

\(=\left(5+5^2\right)+\left(5^3+5^4\right)+\left(5^5+5^6\right)+\left(5^7+5^8\right)\)

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

\(=30+5^2.30+5^4.30+5^6.30\)

\(=30\left(1+5^2+5^4+5^6\right)⋮30\)

\(\Rightarrow A\) là bội của 30 (đpcm)