Question

Cho A = 3+3²+3³+3⁴+...+3⁸⁹+3⁹⁰. Chứng minh A chia hết cho 4.

Answer 1

\(A=\left(3+3^2\right)+\left(3^3+3^4\right)+...+\left(3^{89}+3^{90}\right)\\ A=3\left(1+3\right)+3^3\left(1+3\right)+...+3^{89}\left(1+3\right)\\ A=3\cdot4+3^3\cdot4+...+3^{89}\cdot4\\ A=4\left(3+3^3+...+3^{89}\right)⋮4\)

Answer 2

A = ( 3 + 3 2 ) + ( 3 3 + 3 4 ) + . . . + ( 3 89 + 3 90 )

A = 3 ( 1 + 3 ) + 3 3 ( 1 + 3 ) + . . . + 3 89 ( 1 + 3 )

A = 3 ⋅ 4 + 3 3 ⋅ 4 + . . . + 3 89 ⋅ 4

A = 4 ( 3 + 3 3 + . . . + 3 89 ) ⋮ 4