Question

chứng tỏ A=1+3+3^1+3^2+...+3^100 chia hết cho 4 ?

Answer 1

A = 1 + 3 + 3¹ + 3² + ... + 3¹⁰⁰

A = (1 + 3) + (3¹ + 3²) + ... + (3⁹⁹ + 3¹⁰⁰)

A= 4 + 3.(1 + 3) + ... + 3⁹⁹.(1 + 3)

A = 4 + 3.4 + ... + 3⁹⁹.4

A = 4.(1 + 3 + ... + 3⁹⁹) chia hết cho 4 (đpcm)

Answer 2

Có: A = (1+3) + 3.(1+3) + 3^3.(1+3) + ... + 3^99.(1+3)

      A = 4+3.4+3^3.4+ ... +3^99.4

      A = (1+3+3^3+ ... +3^99).4

=> Achia hết cho 4

Thanks !!!