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A = \(\dfrac{2008}{2009+2010+2011}+\dfrac{2009}{2009+2010+2011}+\dfrac{2010}{2009+2010+2011}\)
Ta có:
\(\dfrac{2008}{2009}>\dfrac{2008}{2009+2010+2011}\)
\(\dfrac{2009}{2010}>\dfrac{2009}{2009+2010+2011}\)
\(\dfrac{2010}{2011}>\dfrac{2010}{2009+2010+2011}\)
Từ 3 điều trên suy ra : A < B
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\(2010^2-2009^2+2008^2-...+2^2-1^2\)
\(=-\left(1^2-2^2+3^2-...+2009^2-2010^2\right)\)
\(=-\left[1^2+2^2+...+2009^2+2010^2-\left(2^2+4^2+...+2010^2\right)\right]\)
\(=-\left[\frac{2010.\left(2010-1\right)\left(2.2010-1\right)}{6}-2^2\left(1^2+2^2+...+1005^2\right)\right]\)
\(=-\left[2704847285-2^2.\frac{1005\left(1005-1\right)\left(2.1005-1\right)}{6}\right]\)
\(=-\left(2704847285-1351414120\right)=1353433165\)
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a, \(\frac{1}{2009}+\frac{2}{2009}+...+\frac{2008}{2009}\\ \frac{\left(1+2008\right)\cdot2008\div2}{2009}=\frac{2017036}{2009}\)
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\(\dfrac{2010}{2009}-\dfrac{2009}{2008}+\dfrac{1}{2008\times2009}\)
\(=\dfrac{2010\times2008}{2008\times2009}-\dfrac{2009\times2009}{2008\times2009}+\dfrac{1}{2008\times2009}\)
\(=\dfrac{2010\times2008-2009\times2009+1}{2008\times2009}\)
\(=\dfrac{\left(2009+1\right)\times2008-2009\times2009+1}{2008\times2009}\)
\(=\dfrac{2009\times2008+2008+1-2009\times2009}{2008\times2009}\)
\(=\dfrac{2009\times2008+2009-2009\times2009}{2008\times2009}\)
\(=\dfrac{2009\times\left(2008+1-2009\right)}{2008\times2009}\)
\(=\dfrac{2009\times0}{2008\times2009}\)
\(=0\)
= 6072 nha bn
Nguyễn Thành Đô
Kết quả là 6027.