= 5^2017( 1+5-5^2)
=5^2017. (-19) chia hết cho 19
\(5^{2017}+5^{2018}-5^{2019}=5^{2017}\left(1+5-5^2\right)=5^{2017}\left(-19\right)⋮19\)
52017 + 52018 + 52019
= 52017 . ( 1 + 5 - 52 )
= 52017 . ( -19) \(⋮\)19
=> 52017 + 52018 - 52019 \(⋮\)19
Ta có :
\(5^{2017}+5^{2018}-5^{2019}\)
\(=5^{2017}\times1+5^{2017}\times5-5^{2017}\times5^2\)
\(=5^{2017}\times\left(1+5-25\right)\)
\(=5^{2017}\times\left(-19\right)⋮19\)
\(\Rightarrow5^{2017}+5^{2018}-5^{2019}⋮19\left(đpcm\right)\)
~Study well~
#KSJ
\(5^{2017}+5^{2018}-5^{2019}\)
\(=5^{2017}+5^{2017}\cdot5-5^{2017}\cdot5^2\)
\(=5^{2017}\left(1+5-5^2\right)\)
\(=5^{2017}\cdot\left(-19\right)⋮19\)
Vậy \(5^{2017}+5^{2018}-5^{2019}⋮19\)
=))
