\(\dfrac{1}{50}-\dfrac{1}{50.49}-\dfrac{1}{49.48}-...-\dfrac{1}{2.1}\)
\(=\dfrac{1}{50}-\dfrac{50-49}{50.49}-\dfrac{49-48}{49.48}-...-\dfrac{2-1}{2.1}\)
\(=\dfrac{1}{50}-\left(\dfrac{1}{49}-\dfrac{1}{50}\right)-\left(\dfrac{1}{48}-\dfrac{1}{49}\right)-...-\left(1-\dfrac{1}{2}\right)\)
\(=\dfrac{1}{50}-\dfrac{1}{49}+\dfrac{1}{50}-\dfrac{1}{48}+\dfrac{1}{49}-...-1+\dfrac{1}{2}\)
\(=\dfrac{1}{50}+\dfrac{1}{50}-1\)
\(=\dfrac{1+1-50}{50}\)
\(=\dfrac{-24}{25}\)
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