Question

[Nguyễn Anh Quân]

a,Cho M= 2020+2020²+...+2020¹⁰

Chứng minh M : 2021 dư 0

b, Cho A= 2021+2021²+...+2021²⁰²⁰

Chứng minh A:2022 dư 0

Answer 1

[Đoàn Đức Hà]

a) \(M=2020+2020^2+...+2020^{10}\)

\(M=\left(2020+2020^2\right)+\left(2020^3+2020^4\right)+...+\left(2020^9+2020^{10}\right)\)

\(M=2020\left(1+2020\right)+2020^3\left(1+2020\right)+...+2020^9\left(1+2020\right)\)

\(M=2021\left(2020+2020^3+...+2020^9\right)⋮2021\).

b) Bạn làm tương tự câu a). 

Answer 2

[Nguyễn Huy Tú]

b, \(A=2021+2021^2+...+2021^{2020}\)

\(=2021\left(1+2021\right)+...+2021^{2019}\left(1+2021\right)\)

\(=2022\left(2021+...+2021^{2019}\right)⋮2022\)

Vậy ta có đpcm