Cho A=(1+3+3^2+…+3^2020).Chứng minh rằng A=(3^2021-1):2

2 bình luận về “Cho A=(1+3+3^2+…+3^2020).Chứng minh rằng A=(3^2021-1):2”

1. Lời giải:
   

   A=1+3+3^2+…+3^2020

   =>3A=3+3^2+3^3+…+3^2021

   =>3A-A=(3+3^2+3^3+…+3^2021)-(1+3+3^2+…+3^2020)

   =>2A=3^2021-1

   =>A=(3^2021-1):2

   Vậy A=(3^2021-1):2

   Trả lời
2. Ta có:

   A=1+3+3^2+…+3^2020

   3A=3(1+3+3^2+…+3^2020)

   3A=3+3^2+3^3+…+3^2021

   3A-A=(3+3^2+3^3+…+3^2021)-(1+3+3^2+…+3^2020)

   2A=3^2021-1

   A=(3^2021-1)/2 (đpcm)

   Trả lời