Question

[luxy]

tính nhanh 1/4+1/12+1/36+1/108+1/324+1/972

Answer 1

[phan ngoc nhi]

Đặt A= 1/4+1/12+1/36+1/108+1/324 +1/972

            =1/4.(1+1/3+1/9+1/27+1/81+1/243)

            =1/4(1+1/3 +1/3^2 +1/3^3 +1/3^4 +1/3^5)

             gọi M=1+1/3+1/3^2+1/3^3+1/3^4+1/3^5

                     3M=3+1+1/3+1/3^2+1/3^3+1/3^4

                     3M-M=(3+1+1/3+1/3^2+1/3^3+1/3^4)-(1+1/3+1/3^2+1/3^3+1/3^4+1/3^5)

                         2M=3-1/3^5

                         M=3/2-1/3^5.2  

                A=1/4.(3/2-1/3^5.2)

                A=3/8-1/1944=91/243

                  Vậy .......

                Chúc bạn học tốt .....^-^