Tính giá trị của$C = 3/2,, + ,,3/8,, + ,,3/32,, + ,,3/128,, — Không quảng cáo

Phương pháp giải

- Tính 4 x C

- Tính 4 x C - C

$C = \frac{3}{2}\,\, + \,\,\frac{3}{8}\,\, + \,\,\frac{3}{{32}}\,\, + \,\,\frac{3}{{128}}\,\, + \,\,\frac{3}{{512}}$

$4 \times C = 4 \times \left( {\frac{3}{2} + \frac{3}{8} + \frac{3}{{32}} + \frac{3}{{128}} + \frac{3}{{512}}} \right)$

$4 \times C = 6 + \frac{3}{2} + \frac{3}{8} + \frac{3}{{32}} + \frac{3}{{128}}$

$4 \times C - C = \left( {6 + \frac{3}{2} + \frac{3}{8} + \frac{3}{{32}} + \frac{3}{{128}}} \right) - \left( {\frac{3}{2} + \frac{3}{8} + \frac{3}{{32}} + \frac{3}{{128}} + \frac{3}{{512}}} \right)$

$3 \times C = 6 - \frac{3}{{512}} = \frac{{3069}}{{512}}$

$C = \frac{{3069}}{{512}}:3 = \frac{{1023}}{{512}}$