Question

Chứng tỏ rằng:

 \(S = 1 + 5 + 5^2 + 5^3 + 5^4 + ...+ 5^{2017}\)    chia hết cho 3

Answer 1

\(S=1+5+5^2+5^3+.......+5^{2017}\)

\(=\left(1+5\right)+\left(5^2+5^3\right)+......+\left(5^{2016}+5^{2017}\right)\)

\(=6+5^2\left(1+5\right)+.........+5^{2016}\left(1+5\right)\)

\(=6+5^2.6+.......+5^{2016}.6=6\left(1+5^2+......+5^{2016}\right)⋮3\)

Answer 2

S=1+5+5²+5³+5⁴+....+5²⁰¹⁷

S=(1+5)+(5²+5³)+(5⁴+5⁵)+.....+(5²⁰¹⁶+5²⁰¹⁷)

S=(1+5)+5².(1+5)+5⁴.(1+5)+...+5²⁰¹⁶.(1+5)

S=6+5².6+5⁴.6+...+5²⁰¹⁶.6

S=6.(1+5²+5⁴+...+5²⁰¹⁶)

S=2.3.(1+5²+5⁴+...+5²⁰¹⁶)\(⋮\)3

Chúc bn học tốt

Answer 3

S= ( 1+5 ) + ( 5^2 + 5^3 ) + ( 5^4 + 5^5 ) + .....+ ( 5^2016 + 5^2017)

S= 6 + ( 5^2 + 5^3 ) + ( 5^4 + 5^5 ) + .....+ ( 5^2016 + 5^2017) chia hết cho 3 

=> S chia hết cho 3