Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
5.29 < 8.32 = {2^3}{.2^5} = {2^{3.5}} = {2^8} < {2^{11}}\\
\Rightarrow 5.29 < {2^{11}}\\
b,\\
S = 1 + 2 + {2^2} + {2^3} + .... + {2^{63}}\\
\Leftrightarrow 2S = 2.\left( {1 + 2 + {2^2} + {2^3} + .... + {2^{63}}} \right)\\
\Leftrightarrow 2S = 2.1 + 2.2 + {2.2^2} + {2.2^3} + ...... + {2.2^{63}}\\
\Leftrightarrow 2S = 2 + {2^2} + {2^3} + {2^4} + ..... + {2^{64}}\\
\Rightarrow 2S - S = \left( {2 + {2^2} + {2^3} + {2^4} + ..... + {2^{64}}} \right) - \left( {1 + 2 + {2^2} + {2^3} + .... + {2^{63}}} \right)\\
\Leftrightarrow S = {2^{64}} - 1\\
S = {2^{64}} - 1 < {2^{64}} = {2^{2 + 62}} = {2^2}{.2^{62}} = {4.2^{62}} < {5.2^{62}}\\
\Rightarrow S < {5.2^{62}}
\end{array}\)
