Đáp án:
Giải thích các bước giải:
\[\begin{array}{l}
A = - \frac{1}{3} + \frac{1}{{{3^2}}} - \frac{1}{{{3^3}}} + ..... + \frac{1}{{{3^{50}}}} - \frac{1}{{{3^{51}}}}\\
\Leftrightarrow 3A = - 1 + \frac{1}{3} - \frac{1}{{{3^2}}} + .... + \frac{1}{{{3^{49}}}} - \frac{1}{{{3^{50}}}}\\
\Leftrightarrow 3A + A = \left( { - 1 + \frac{1}{3} - \frac{1}{{{3^2}}} + .... + \frac{1}{{{3^{49}}}} - \frac{1}{{{3^{50}}}}} \right) + \left( { - \frac{1}{3} + \frac{1}{{{3^2}}} - \frac{1}{{{3^3}}} + .... + \frac{1}{{{3^{50}}}} - \frac{1}{{{3^{51}}}}} \right)\\
\Leftrightarrow 4A = - 1 - \frac{1}{{{3^{51}}}}\\
\Leftrightarrow 4A = - \frac{{{3^{51}} + 1}}{{{3^{51}}}} \Rightarrow A = - \frac{{{3^{51}} + 1}}{{{{4.3}^{51}}}}
\end{array}\]
