\(\begin{array}{l}
A = 2 + {2^2} + ....... + {2^{99}}\\
\Rightarrow 2A = 2\left( {2 + {2^2} + ...... + {2^{99}}} \right) = {2^2} + {2^3} + .... + {2^{100}}\\
\Rightarrow 2A - A = {2^2} + {2^3} + .... + {2^{100}} - \left( {2 + {2^2} + ....... + {2^{99}}} \right)\\
\Leftrightarrow A = {2^{100}} - 2\\
Ta\,\,co:\,\,\,{\left( {...2} \right)^{20}} = \overline {...76} \\
\Rightarrow {2^{100}} = {\left[ {{{\left( {...2} \right)}^{20}}} \right]^5} = {\left( {\overline {...76} } \right)^5} = \overline {...76} \\
\Rightarrow {2^{100}} - 2 = \overline {...76} - 2 = \overline {...74} \\
\Rightarrow A\,\,\,co\,\,\,chu\,\,\,\,so\,\,\,\tan \,\,cung\,\,\,la\,\,\,74.
\end{array}\)
