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

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

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

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

S = 2010 + 2010^2 + ........ + 2010^2010

   = ( 2010 + 2010^2) + ....... + ( 2010^2009 + 2010^2010 )

   = 2010. ( 1 + 2010 ) + .........+ 2010^2009. ( 1 + 2010 )

   = 2010.2011 + ....... + 2010^2009.2011 chia hết cho 2011

=> S chia hết cho 2011

A = 2010²⁰¹¹ - 2010²⁰¹⁰

A = 2010²⁰¹⁰ .( 2010 - 1)

A = 2010²⁰¹⁰.2009

2009 ⋮ 2009 ⇒ A = 2010²⁰¹⁰.2009 ⋮ 2009

Có : \(2009+2010>\dfrac{2009}{2010}\) ; \(2011+2012>\dfrac{2011}{2012}\)

\(\dfrac{2011}{2010}>1\) ; \(\dfrac{2010}{2011}< 1\) \(\Rightarrow\dfrac{2011}{2010}>\dfrac{2010}{2011}\)

Ta có : \(2009+2010+\dfrac{2011}{2010}+2011+2012>\dfrac{2009}{2010}+\dfrac{2010}{2011}+\dfrac{2011}{2012}\)

\(\Leftrightarrow B>A\)

Hay \(A< B\)

bạn có chắc là bài làm của bạn đúng ko ?

M= ( 1+2010¹)+(2010²+2010³)+(2010⁴+2010⁵)+(2010⁶+2010⁷)

M= 1.(2010+1) + 2012².(2010+1)+2010⁴.(2010+1)+2010⁶.(2010+1)

M= 2011.(1+2012²+2010⁴+2010⁶)

Vậy M chia hết cho 2011

\(B=\dfrac{2008+2009+2010}{2009+2010+2011}=\dfrac{2008}{2009+2010+2011}+\dfrac{2009}{2009+2010+2011}+\dfrac{2010}{2009+2010+2011}\)Ta có : \(\dfrac{2008}{2009}>\dfrac{2008}{2009+2010+2011}\)

\(\dfrac{2009}{2010}>\dfrac{2009}{2009+2010+2011}\)

\(\dfrac{2010}{2011}>\dfrac{2010}{2009+2010+2011}\)\(=>\dfrac{2008}{2009}+\dfrac{2009}{2010}+\dfrac{2010}{2011}>\dfrac{2008+2009+2010}{2009+2010+2011}\)

Hay A > B

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