Question

Cho A=1+3+3²+3³+3⁴+...+3^11

Chứng to A chia hết cho 13

 

 

Answer 1

A = 1 + 3 + 3² + 3³ + ...... + 3¹¹

=> 3A = 3 + 3² + 3³ + ...... + 3¹²

=> 3A - A = 3¹² - 1

=> 2A = 3¹² - 1

=> A = \(\frac{3^{12}-1}{2}\)

Answer 2

A= (1+3+3²) + (3³+3⁴+3⁵)+..... +(3⁹+3¹⁰+3¹¹)

A= 13+ 3³. (1+3+3²) +......+3⁹. (1+3+3²)

A= 13+3³.13+3⁶.13+3⁹.13

=> Achia hêt cho 13