Đáp án:
$S = \frac{{3280}}{{2187}}$
Giải thích các bước giải:
$\begin{array}{l}
S = 1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{{27}} + ... + \frac{1}{{2187}}\\
\Rightarrow 3 \times S = 3 \times 1 + 3 \times \frac{1}{3} + 3 \times \frac{1}{9} + 3 \times \frac{1}{{27}} + ... + 3 \times \frac{1}{{2187}}\\
\Rightarrow 3S = 3 + 1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{{27}} + ... + \frac{1}{{729}}\\
\Rightarrow 3S - S = \left( {3 + 1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{{27}} + ... + \frac{1}{{729}}} \right) - \left( {1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{{27}} + ... + \frac{1}{{2187}}} \right)\\
\Rightarrow 2S = 3 - \frac{1}{{2187}} = \frac{{3 \times 2187 - 1}}{{2187}} = \frac{{6560}}{{2187}}\\
\Rightarrow S = \frac{{3280}}{{2187}}\\
\end{array}$
