Question

[Nguyễn Ngọc Lan]

Tính bằng cách thuận tiện nhất:

 A = 1/3+ 1/9+ 1/27+ 1/81+ 1/243+ 1/729

Answer 1

[Đoàn Đức Hà]

\(A=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)

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

\(3\times A-A=\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\right)-\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\right)\)

\(2\times A=1-\frac{1}{729}=\frac{728}{729}\)

\(A=\frac{364}{729}\)