Đáp án:
\(\dfrac{910}{243}\)
Giải thích các bước giải:
\[\begin{array}{l}
A = \frac{5}{2} + \frac{5}{6} + \frac{5}{{18}} + \frac{5}{{54}} + \frac{5}{{162}} + \frac{5}{{486}}\\
3 \times A = \frac{{5 \times 3}}{2} + \frac{{5 \times 3}}{6} + \frac{{5 \times 3}}{{18}} + \frac{{5 \times 3}}{{54}} + \frac{{5 \times 3}}{{162}} + \frac{{5 \times 3}}{{486}}\\
3 \times A = \frac{{15}}{2} + \frac{5}{2} + \frac{5}{6} + \frac{5}{{18}} + \frac{5}{{54}} + \frac{5}{{162}}\\
3 \times A - A = \frac{{15}}{2} - \frac{5}{{486}}\\
2 \times A = \frac{{1820}}{243}\\
A = \frac{{910}}{243}
\end{array}\]
