수악중독

\(S = {\dfrac{2}{{1 \cdot \left( {1 + 2} \right)}}} +{\dfrac{{{2^2}}}{{\left( {1 + 2} \right) \cdot \left( {1 + 2 + {2^2}} \right)}}} + {\dfrac{{{2^3}}}{{\left( {1 + 2 + {2^2}} \right) \cdot \left( {1 + 2 + {2^2} + {2^3}} \right)}}} \) \(+ \cdots + {\dfrac{{{2^{100}}}}{{\left( {1 + 2 + {2^2} + \cdots {2^{99}}} \right) \cdot \left( {1 + 2 + {2^2} + \cdots + {2^{100}}} \right)}}}\) 의 값을 기약분수로 나타내면..