b: \(N=\dfrac{1}{1\cdot5}+\dfrac{1}{5\cdot10}+...+\dfrac{1}{2005\cdot2010}\)
\(=\dfrac{1}{5}\left(1-\dfrac{1}{2010}\right)\)
\(=\dfrac{1}{5}\cdot\dfrac{2009}{2010}=\dfrac{2009}{10050}\)
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