Đáp án:
$\begin{array}{l}
S = \dfrac{1}{{{2^2}}} - \dfrac{1}{{{2^4}}} + \dfrac{1}{{{2^6}}} - ... + \\
+ \dfrac{1}{{{2^{4n - 2}}}} - \dfrac{1}{{{2^{4n}}}} + ... + \dfrac{1}{{{2^{2002}}}} - \dfrac{1}{{{2^{2004}}}}\\
\Rightarrow {2^2}.S = 1 - \dfrac{1}{{{2^2}}} + \dfrac{1}{{{2^4}}} + ... + \dfrac{1}{{{2^{4n}}}} + ...\\
+ \dfrac{1}{{{2^{2000}}}} - \dfrac{1}{{{2^{2002}}}}\\
\Rightarrow 4S + S = 5S = 1 - \dfrac{1}{{{2^{2004}}}}\\
\Rightarrow S = \dfrac{1}{5} - \dfrac{1}{{{{5.2}^{2004}}}} < \dfrac{1}{5}\\
\Rightarrow S < 0,2
\end{array}$
Vậy S<0,2
