Tính nhanh: 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243
Tính nhanh: \(1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{{27}} + \frac{1}{{81}} + \frac{1}{{243}}\).
Đặt \(S = 1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{{27}} + \frac{1}{{81}} + \frac{1}{{243}}\)
\(3S = 3 + 1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{{27}} + \frac{1}{{81}}\)
\(3S - S = 3 - \frac{1}{{243}}\)
\(2S = \frac{{728}}{{243}}\)
\(S = \frac{{728}}{{243}}:2\)
Vậy \(S = \frac{{364}}{{243}}\)