Tính giá trị$A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 +. . . . + — Không quảng cáo

Phương pháp giải

- Tính A x 2

- Tính A x 2 - A

$A = \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + \frac{1}{{32}} + .... + \frac{1}{{1024}}$

$2 \times A = \frac{2}{2} + \frac{2}{4} + \frac{2}{8} + \frac{2}{{16}} + \frac{2}{{32}} + .... + \frac{2}{{1024}}$

$2 \times A = 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + .... + \frac{1}{{512}}$

$2 \times A - A = \left( {1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + .... + \frac{1}{{512}}} \right) - \left( {\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + ... + \frac{1}{{1024}}} \right)$

$A = 1 - \frac{1}{{1024}} = \frac{{1023}}{{1024}}$