Question

Cho A = 1+3+3²+3³+3⁴+...+3¹⁹⁹⁹+3²⁰⁰⁰ .chứng tỏ rằng A chia hết cho 13

Answer 1

Ta có: A = 1 + 3 + 3² + 3³ + 3⁴ +......+ 3¹⁹⁹⁹ + 3²⁰⁰⁰

=> A = (1 + 3 + 3²) + (3³ + 3⁴ + 3⁵) +......+ (3¹⁹⁹⁸ + 3¹⁹⁹⁹ + 3²⁰⁰¹)

=> A = 1.13 + 3³.(1 + 3 + 9) + ..... + 3¹⁹⁹⁸.( 1 + 3 + 9)

=> A = 13.1 + 3.13 + .... + 3¹⁹⁹⁸.13

=> A = 13.( 1 + 3³ + .... + 3¹⁹⁹⁸) chia hết cho 13

Answer 2

Dan chung A chia het cho 13

A= (1+3+3^2)+(3^3+3^4+3^5)+...+(3^1998+3^1999+3^2000)

Co 667 cap 4 luy thua

A=13+3^3.13+...+3^1998.13

A=13(1+3^3+...+3^1998) chia het cho 13

k cho minh nhe!