Question

Chứng Tỏ S chia hết cho 2011

S=(2010+2010²)+(2010³+2010⁴)+...+(2010²⁰⁰⁹+2010²⁰¹⁰)

Giúp mik với Mình đang cần gấp !!!

Answer 1

dễ ợt

s=2010(1+20100+2010^3(1+2010)+............+2010^2009(1+2010)

s=2010.2011+2010^3.2011+.........+2010^2009.2011

s=2011(2010+2010^3+.......+2010^2009) chia hết cho 2011

Answer 2

 \(S=\left(2010+2010^2\right)+\left(2010^3+2010^4\right)+...+\left(2010^{2009}+2010^{2010}\right)\)

\(S=2010\left(2010+1\right)+2010^3\left(2010+1\right)+...+2010^{2009}\left(2010+1\right)\)

 \(S=2011.\left(2010+2010^3+2010^5+...+2010^{2009}\right)\) chia hết cho 2011