1.
a) 53/101 . -13/97 + 53/101 . -84/97 b) (1/57 - 1/5757 + 1/23) (1/2 - 1/3 - 1/6)
= 53/101 . {(-13 - 84) / 97} = (1/57 - 1/5757 + 1/23) (1/6 - 1/6)
= 53/101 . (-1) = (1/57 - 1/5757 + 1/23) . 0
= -53/101 = 0
c) (1 + 1/2) (1 + 1/3) (1 + 1/4) ... (1 + 1/2020) (1 + 1/2021)
= 3/2 . 4/3 . 5/4 ... 2021/2020 . 2022/2021
= 2022/2 = 1011
d) (1 - 1/2) (1 - 1/3) (1 - 1/4) ... (1 - 1/2020) (1 - 1/2021)
= 1/2 . 2/3 . 3/4 ... 2019/2020 . 2020/2021
= 1/2021