Tính giá trịA = 1/5 + 1/10 + 1/20 + 1/40 + 1/80 + 1/160 +

Đề bài

Tính giá trị $A = \frac{1}{5} + \frac{1}{{10}} + \frac{1}{{20}} + \frac{1}{{40}} + \frac{1}{{80}} + \frac{1}{{160}} + \frac{1}{{320}}$

Phương pháp giải

- Tính 2 x A

- Tính 2 x A - A

$A = \frac{1}{5} + \frac{1}{{10}} + \frac{1}{{20}} + \frac{1}{{40}} + \frac{1}{{80}} + \frac{1}{{160}} + \frac{1}{{320}}$

$2 \times A = \frac{2}{5} + \frac{2}{{10}} + \frac{2}{{20}} + \frac{2}{{40}} + \frac{2}{{80}} + \frac{2}{{160}} + \frac{2}{{320}}$

$2 \times A = \frac{2}{5} + \frac{1}{5} + \frac{1}{{10}} + \frac{1}{{20}} + \frac{1}{{40}} + \frac{1}{{80}} + \frac{1}{{160}}$

$2 \times A - A = \frac{2}{5} - \frac{1}{{320}}$

$A = \frac{{127}}{{320}}$