Question

Cho A=2+\(2^2\)+\(2^3\)+.....+\(2^{100}\)

a, Chứng minh A \(⋮3\).

b, Chứng ming A \(⋮5\).

Answer 1

a, A= 2 + 2² + 2³ +...+ 2¹⁰⁰

A= ( 2+2² ) + ( 2³+2⁴ ) +...+( 2⁹⁹ + 2¹⁰⁰ )

A= 6+ 2² ( 2+2²)+ ...+ 2⁹⁸ (2+2²)

A=6+ 2².6+ ...+ 2⁹⁸.6

A= 6.(2²+...+2⁹⁸) chia hết cho 3 ( vì 6 chia hết cho 3)

Answer 2

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

\(=3\left(2+2^3+...+2^{99}\right)⋮3\)

b: \(A=2\left(1+2+2^2+2^3\right)+2^5\left(1+2+2^2+2^3\right)+...+2^{97}\left(1+2+2^2+2^3\right)\)

\(=15\left(2+2^5+...+2^{97}\right)⋮5\)