Question

Chứng tỏ:

a) A ⋮ 3 với A = 2 + 2² + 2³ + 2⁴ + ... + 2¹⁰⁰

b) B ⋮ 5 với B = 4 + 4² + 4³ + ... + 4²⁰²²

 

Answer 1

a: Ta có: \(A=2+2^2+2^3+2^4+...+2^{100}\)

\(=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{99}\left(1+2\right)\)

\(=3\cdot\left(2+2^3+...+2^{99}\right)⋮3\)

b: Ta có: \(B=4+4^2+4^3+...+4^{2022}\)

\(=4\left(1+4\right)+4^3\left(1+4\right)+...+4^{2021}\left(1+4\right)\)

\(=5\cdot\left(4+4^3+...+4^{2021}\right)⋮5\)

Answer 2

a)\(A=2+2^2+2^3+2^4+...+2^{100}=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{99}\left(1+2\right)=3.2+3.2^3+...+3.2^{99}=3\left(2+2^3+...+2^{99}\right)⋮3\)b) \(B=4+4^2+4^3+...+4^{2022}=4\left(1+4\right)+4^3\left(1+4\right)+...+4^{2021}\left(1+4\right)=5.4+5.4^3+...+5.4^{2021}=5\left(4+4^3+...+4^{2021}\right)⋮5\)