Tính: a) S = C 0 2022 9^2022 + C 1 2022 9^2021 + + C k 2022 9^(2022 - k) + + C 2021 2022 9 + C 2022 2022
Giải thích
Áp dụng công thức nhị thức Newton ta có:
a) S=C2022092022+C2022192021+...+C2022k92022−k+...+C202220219+C20222022
=C2022092022+C2022192021 . 1+...+C2022k92022−k.1k+...+C202220219.12021+C20222022.12022
=9+12020=102022.
b) T=C2022042022−C2022142021 . 3+...−C202220214 . 32021+C2022202232022
=C2022042022+C2022142021 .−31+...+C202220214 . −32021+C20222022−32022
=4+−32022=12022=1.