a.1/1.2+1/2.3+1/3.4+...+1/2019.2020
=1-1/2+1/3-1/4+...+1/2019-1/2020
=1-1/2020
=2019/2020
b.1/1.3+1/3.5+1/5.7+...+1/2019.2021
=1/2.2(1/1.3+1/3.5+1/5.7+...+1/2019.2021)
=1/2.(2/1.3+2/3.5+2/5.7+...+2/2019.2021)
=1/2.(1-1/3+1/3-1/5+1/5-1/7+...+1/2019.1/2021)
=1/2.(1-1/2021)
=1/2.2020/2021
=2020/4042
=1010/2021