b: =1-1/2+1/2-1/3+...+1/2021-1/2022
=2021/2022
a: \(=\dfrac{1}{4}\left(\dfrac{4}{1\cdot5}+\dfrac{4}{5\cdot9}+...+\dfrac{4}{81\cdot85}\right)\)
\(=\dfrac{1}{4}\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{81}-\dfrac{1}{85}\right)\)
\(=\dfrac{1}{4}\cdot\dfrac{84}{85}=\dfrac{21}{85}\)