\(\dfrac{1}{100.99}-\dfrac{1}{99.98}-\dfrac{1}{98.97}-...-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)
\(=\dfrac{1}{100}-\dfrac{1}{99}+\dfrac{1}{99}-\dfrac{1}{98}+\dfrac{1}{98}-\dfrac{1}{97}+...+\dfrac{1}{3}-\dfrac{1}{2}+\dfrac{1}{2}-1\)
\(=\dfrac{1}{100}-1\)
\(=-\dfrac{99}{100}\)