Question

[Nguyễn Mai Phương]

Tính bằng cách thuận tiện nhất

1/2 + 1/6 + 1/18 + 1/54 + 1/162 + 1/486

Answer 1

[Đoàn Đức Hà]

\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}+\frac{1}{486}\)

\(3\times A=\frac{3}{2}+\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}\)

\(3\times A-A=\left(\frac{3}{2}+\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}\right)-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}+\frac{1}{486}\right)\)

\(2\times A=\frac{3}{2}-\frac{1}{486}\)

\(A=\frac{182}{243}\)

Answer 2

[Trần Quỳnh Chi]

182/243