Question

cho S=5+5^2+5^3+5^4+5^5+5^6+5^7+5^8+5^9+5^10

chứng tỏ S chia hết cho 30

Answer 1

S=5+5^2+5^3+5^4+5^5+5^6+5^7+5^8+5^9+5^10

=>S=(5+5^2)+(5^3+5^4)+(5^5+5^6)+(5^7+5^8)+(5^9+5^10)

=>S=30+5^2(5+5^2)+5^4(5+5^2)+5^6(5+5^2)+5^8(5+5^2)

=>S=30+5^2.30+5^4.30+5^6.30+5^8.30

=>S=30(1+5^2+5^4+5^6+5^8)=> S chia hết cho 30

Answer 2

\(5+5^2+5^3+5^4+5^5+...+5^9+5^{10}\)

\(=5+5^2+5^2\left(5+5^2\right)+5^4\left(5+5^2\right)+...+5^8\left(5+5^2\right)\)

\(=\left(5+5^2\right)\left(1+5^2+5^4+5^6+5^8\right)\)

\(=30.\left(1+5^2+5^4+5^6+5^8\right)\)

vậy S chia hết cho 30 

ko hiểu họi lại mik 

tick mik nka