\(\dfrac{1}{99}-\dfrac{1}{99.98}-\dfrac{1}{98.97}-\dfrac{1}{97.96}-...-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)
\(=\dfrac{1}{99}-\left({\dfrac{1}{98}-\dfrac{1}{99}}\right)-\left({\dfrac{1}{97}-\dfrac{1}{98}}\right)-\left({\dfrac{1}{96}-\dfrac{1}{97}}\right)-...-\left({\dfrac{1}{2}-\dfrac{1}{3}}\right)-\left({1-\dfrac{1}{2}}\right)\)
\(=\dfrac{1}{99}-\dfrac{1}{98}+\dfrac{1}{99}-\dfrac{1}{97}+\dfrac{1}{98}-\dfrac{1}{96}+\dfrac{1}{97}...-\dfrac{1}{2}+\dfrac{1}{3}-1+\dfrac{1}{2}\)
\(=\dfrac{1}{99}+\dfrac{1}{99}-1\)
\(=\dfrac{2}{99}-1\)
\(=\dfrac{-97}{99}\).
