\(A=\dfrac{2004}{2003^2+1}+\dfrac{2004}{2003^2+2}+\dfrac{2004}{2003^2+3}\)
\(\Rightarrow A=2004.\left(\dfrac{1}{2003^2+1}+\dfrac{1}{2003^2+2}+\dfrac{1}{2003^2+3}\right)\)
Ta lại có :
\(0< \dfrac{1}{2003^2+1};\dfrac{1}{2003^2+2};\dfrac{1}{2003^2+3}< 1\)
\(\Rightarrow\left(\dfrac{1}{2003^2+1};\dfrac{1}{2003^2+2};\dfrac{1}{2003^2+3}\right)\in Q^+\)
mà \(2004\in Z^+\)
\(2004\) không chia chết cho \(2003^2+1;2003^2+2;2003^2+3\)
\(\Rightarrow A=2004.\left(\dfrac{1}{2003^2+1}+\dfrac{1}{2003^2+2}+\dfrac{1}{2003^2+3}\right)\in Q^+\)
\(\Rightarrow dpcm\)
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