\(5+5^2+5^3+5^4+5^5+5^6+5^7+5^8+5^9\)
\(=\left(5+5^2+5^3\right)+\left(5^4+5^5+5^6\right)+\left(5^7+5^8+5^9\right)\)
\(=5\times\left(1+5+5^2\right)+5^4\times\left(1+5+5^2\right)+5^7\times\left(1+5+5^2\right)\)
\(=5\times31+5^4\times31+5^7\times31\)
\(=31\times\left(5+5^4+5^7\right)⋮31\)
Vậy tổng trên chia hết cho 31
Bài làm :
Ta có :
\(5+5^2+5^3+5^4+5^5+5^6+5^7+5^8+5^9\)
\(=\left(5+5^2+5^3\right)+\left(5^4+5^5+5^6\right)+\left(5^7+5^8+5^9\right)\)
\(=5\times\left(1+5+5^2\right)+5^4\times\left(1+5+5^2\right)+5^7\times\left(1+5+5^2\right)\)
\(=5\times31+5^4\times31+5^7\times31\)
\(=31\times\left(5+5^4+5^7\right)⋮31\)
=> Điều phải chứng minh
(1+5^2+5^4+5^6+5^8).x=5+5^3+5^5+ ... 5^9
mình cần gấp
