1/3+1/9+1/27+1/81+…+1/19683+1/59049

2 bình luận về “1/3+1/9+1/27+1/81+…+1/19683+1/59049”

1. Đặt: A=1/3+1/9+1/27+1/81+…+1/19683+1/59049

   =1/3+1/3^2+1/3^3+1/3^4+…+1/3^9+1/3^10

   3A=1+1/3+1/3^2+…+1/3^9

   3A-A=(1+1/3+…+1/3^9)-(1/3+1/3^2+…+1/3^10)

   2A=1-1/3^10

     A=(1- 1/3^10)/2

   *** $nhatminhbuithien2010$

    

   Trả lời
2. Giải đáp:

   A=(3^10-1)/(2.3^10).

   Lời giải và giải thích chi tiết:

   Đặt A=1/3+1/9+1/27+1/81+……+1/19683+1/59059

   A=1/3+1/3^2+1/3^3+1/3^4+…..+1/3^9+1/3^10

   3A=1+1/3+1/3^2+1/3^3+……+1/3^8+1/3^9

   3A-A=1+1/3+1/3^2+1/3^3+……+1/3^8+1/3^9-(1/3+1/3^2+1/3^3+1/3^4+…..+1/3^9+1/3^10)

   2A=1-1/3^10

   2A=(3^10-1)/3^10

   A=(3^10-1)/(2.3^10).

   Trả lời