Question

chứng tỏ :

A = 3¹ + 3^{2 +} 3³  + ... + 3⁶⁰  chia hết cho 13

Answer 1

ta co:1+3+3²+3³+.........+3⁶⁰

=(1+3)+(3²+3³)+.....+(3⁵⁹ +3⁶⁰)

=4+(3².1+3³.3)+......+(3⁵⁹.1+3⁵⁹.3)

=4+3².(1+3)+.....+3⁵⁹.(1+3)

=4+3².4+.....+3⁵⁹.4chia het cho 4

hinh nhu de sai

 

Answer 2

 3 + 3² + 3³ + ... + 3⁶⁰

=(3+3²+3³)+(3⁴+3⁵+3⁶)+...+(3⁵⁸+3⁵⁹+3⁶⁰)

=3(1+3+3²)+3⁴(1+3+3²)+...+3⁵⁸(1+3+3²)

=3.(1+3+9)+3⁴(1+3+9)+...+3⁵⁸(1+3+9)

=(1+3+9)(3+3⁴+...+3⁵⁸)

=13(3+3⁴+...+3⁵⁸) chia hết cho 13