S=2²⁰¹⁰-2²⁰⁰⁹-2²⁰⁰⁸-...-2-1

=> 2S=2. 2²⁰¹⁰ -2. 2²⁰⁰⁹-2. 2²⁰⁰⁸-....-2.2-2.1

2S=2^2011-2²⁰¹⁰-2²⁰⁰⁹-....-2²-2

- S=2^2010-2²⁰⁰⁹-2²⁰⁰⁸-...-2-1

=>S=2^2011-1

cai gi ma tum lum the

chịu! bye

\(S=-\left(1+2+...+2^{2009}+2^{2010}\right)\)

\(-2S=2\left(1+2+...+2^{2009}+2^{2010}\right)\)

\(\Rightarrow-2S+S=-S=2+2^2+...+2^{2010}+2^{2011}-1-2-...-2^{2009}-2^{2010}\)

\(-S=2^{2011}-1\Rightarrow S=1-2^{2011}\)

S=2²⁰¹⁰ - 2²⁰⁰⁹ - 2^{2008 -...-2-1}

=>2S=2 x 2²⁰¹⁰ - 2 x 2²⁰⁰⁹ - 2 x 2²⁰⁰⁸ -...-2 x 2 -2 x 1

2S=2²⁰¹¹ - 2²⁰¹⁰ - 2²⁰⁰⁹ - ... - 2² -2

=>S=1-2²⁰¹¹

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

bằng nhau bạn nhé

lộn

\(S=2^{2010}-2^{2009}-...-2-1\)

\(2S=2^{2011}-2^{2010}-2^{2009}-....-2^2-2\)

Trừ dưới cho trên:

\(S=2^{2011}-2.2^{2010}+1=2^{2011}-2^{2011}+1=1\)

\(2010^2-2009^2+2008^2-...+2^2-1^2\)

\(=-\left(1^2-2^2+3^2-...+2009^2-2010^2\right)\)

\(=-\left[1^2+2^2+...+2009^2+2010^2-\left(2^2+4^2+...+2010^2\right)\right]\)

\(=-\left[\frac{2010.\left(2010-1\right)\left(2.2010-1\right)}{6}-2^2\left(1^2+2^2+...+1005^2\right)\right]\)

\(=-\left[2704847285-2^2.\frac{1005\left(1005-1\right)\left(2.1005-1\right)}{6}\right]\)

\(=-\left(2704847285-1351414120\right)=1353433165\)

 2010×2010 - 2009×2009 +2008×2008-...+2×2-1×1

=2 x 2010 - 2 x 2009 + .......+ 2 x 2 - 2 x 1

=2x(2010-2009+2008-.......+2-1)

=2x[(2010-2019)+......+(2-1)]

=2x ( 1+ 1+....+1)

=2x1005

=2010