Mình làm câu a) nha!!!

+) \(A=2009^{2010}+2009^{2009}\)

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

        \(=2009^{2009}.2010\)

+) \(B=2010^{2010}=2010^{2009}.2010\)

Vì \(2010^{2009}>2009^{2009}\)nên \(2010^{2009}.2010>2009^{2009}.2010\)hay \(B>A\)

Vậy \(A< B\)

Hok tốt nha^^

ta có: \(A=\frac{2009^{10}+2}{2009^{11}+2}< 1\)

\(B=\frac{2009^{12}+2}{2009^{12}+2}=1\)

\(\Rightarrow A< B\)

\(A=\frac{2009^{10}+1}{2009^{11}+2}\)            \(B=\frac{2009^{12}+2}{2009^{12}+2}\)

Ta có A< 1 mà B=1 => A<B

\(\frac{1}{41}+\frac{1}{42}+\frac{1}{43}+.....+\frac{1}{80}\)

\(=\left(\frac{1}{41}+\frac{1}{42}+\frac{1}{43}+\frac{1}{44}+.....+\frac{1}{60}\right)+\left(\frac{1}{61}+\frac{1}{62}+......+\frac{1}{80}\right)\)

\(>\left(\frac{1}{60}+\frac{1}{60}+\frac{1}{60}+.....+\frac{1}{60}\right)+\left(\frac{1}{80}+\frac{1}{80}+\frac{1}{80}+.....+\frac{1}{80}\right)\)

\(=\frac{1}{3}+\frac{1}{4}\)

\(=\frac{7}{12}\)

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

\(< \frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}=A\)

sẽ bằng nhau 

câu hỏi tương tự

Ta có :

$B=\genfrac{}{}{0ex}{}{2009^{2010}-2}{2009^{2011}-2}<1$

$\iff B<\genfrac{}{}{0ex}{}{2009^{2010}-2+2011}{2009^{2011}-2+2011}=\genfrac{}{}{0ex}{}{2009^{2010}+2009}{2009^{2011}+2009}=\genfrac{}{}{0ex}{}{2009\left(2009^{2009}+1\right)}{2009\left(2009^{2010}+1\right)}=\genfrac{}{}{0ex}{}{2009^{2009}+1}{2009^{2010}+1}=A$

$\iff A>B$

Ta có :

\(B=\dfrac{2009^{2010}-2}{2009^{2011}-2}< 1\)

\(\Leftrightarrow B< \dfrac{2009^{2010}-2+2011}{2009^{2011}-2+2011}=\dfrac{2009^{2010}+2009}{2009^{2011}+2009}=\dfrac{2009\left(2009^{2009}+1\right)}{2009\left(2009^{2010}+1\right)}=\dfrac{2009^{2009}+1}{2009^{2010}+1}=A\)

\(\Leftrightarrow A>B\)