Question

tính bằng cách hợp lý

1/3+1/9+1/27+1/81+1/243

 

Answer 1

Đặt A= 1/3+1/9+1/27+1/81+1/243

A= 1/3+1/3^2+1/3^3+1/3^4+1/3^5

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

3A-A=1+1/3+1/3^2+1/3^3+1/3^4-1/3-1/3^2-1/3^3-1/3^4-1/3^5

2A=1-1/3^5

2A=242/243

A=121/243

Answer 2

ta bằng 121/243

duyệt nha

Answer 3

\(A=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)

\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+\frac{1}{3^5}\)

\(3A=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}\)

\(3A-A=1-\frac{1}{3^5}\)

\(2A=1-\frac{1}{3^5}\)

\(A=\frac{1-\frac{1}{3^5}}{2}=\frac{1-\frac{1}{243}}{2}=\frac{121}{243}\)