Đề bài
Tính giá trị của $D = \frac{5}{2}\,\, + \frac{5}{6}\,\, + \,\,\frac{5}{{18}}\,\, + \,\,\frac{5}{{54}}\,\, + \,\,\frac{5}{{162}}\,\, + \,\,\frac{5}{{486}}$
Phương pháp giải
- Tính 3 x D
- Tính 3 x D - D
$D = \frac{5}{2}\,\, + \frac{5}{6}\,\, + \,\,\frac{5}{{18}}\,\, + \,\,\frac{5}{{54}}\,\, + \,\,\frac{5}{{162}}\,\, + \,\,\frac{5}{{486}}$
$3 \times D = 3 \times \left( {\frac{5}{2} + \frac{5}{6} + \frac{5}{{18}} + \frac{5}{{54}} + \frac{5}{{162}} + \frac{5}{{486}}} \right)$
$3 \times D = \frac{{15}}{2} + \frac{5}{2} + \frac{5}{6} + \frac{5}{{18}} + \frac{5}{{54}} + \frac{5}{{162}}$
$3 \times D - D = \frac{{15}}{2} - \frac{5}{{486}}$
$2 \times D = \frac{{1820}}{{243}}$
$D = \frac{{1820}}{{243}}:2 = \frac{{910}}{{243}}$