Tính giá trị của$C = \frac{3}{2}\,\, + \,\,\frac{3}{8}\,\, + \,\,\frac{3}{{32}}\,\, + \,\,\frac{3}{{128}}\,\, + \,\,\frac{3}{{512}}$

Phương pháp giải

- Tính 4 x C - Tính 4 x C - C

Lời giải của GV ufa999.cc

$C = \frac{3}{2}\,\, + \,\,\frac{3}{8}\,\, + \,\,\frac{3}{{32}}\,\, + \,\,\frac{3}{{128}}\,\, + \,\,\frac{3}{{512}}$ $4 \times C = 4 \times \left( {\frac{3}{2} + \frac{3}{8} + \frac{3}{{32}} + \frac{3}{{128}} + \frac{3}{{512}}} \right)$ $4 \times C = 6 + \frac{3}{2} + \frac{3}{8} + \frac{3}{{32}} + \frac{3}{{128}}$ $4 \times C - C = \left( {6 + \frac{3}{2} + \frac{3}{8} + \frac{3}{{32}} + \frac{3}{{128}}} \right) - \left( {\frac{3}{2} + \frac{3}{8} + \frac{3}{{32}} + \frac{3}{{128}} + \frac{3}{{512}}} \right)$ $3 \times C = 6 - \frac{3}{{512}} = \frac{{3069}}{{512}}$ $C = \frac{{3069}}{{512}}:3 = \frac{{1023}}{{512}}$