Giải thích các bước giải:
\(\begin{array}{l}
15.S = {2^{12}}C_{12}^0 + {2^{10}}.C_{12}^2 + ... + C_{12}^{12} = C_{12}^0 + {2^2}.C_{12}^2 + ... + {2^{12}}C_{12}^{12}\\
{S_1} = C_{12}^0 + 2.C_{12}^1 + ... + {2^{11}}C_{12}^{11} + {2^{12}}C_{12}^{12} = {(2 + 1)^{12}} = {3^{12}}\\
{S_2} = C_{12}^0 - 2.C_{12}^1 + ... - {2^{11}}C_{12}^{11} + {2^{12}}C_{12}^{12} = {(2 - 1)^{12}} = 1\\
S = \frac{{{S_1} + {S_2}}}{2} = \frac{{{3^{12}} + 1}}{2}\\
16.\\
{S_1} = C_{20}^0 + 5C_{20}^1 + ... + {5^{19}}.C_{20}^{19} + {5^{20}}.C_{20}^{20} = {(5 + 1)^{20}} = {6^{20}}\\
{S_2} = C_{20}^0 - 5C_{20}^1 + ... - {5^{19}}.C_{20}^{19} + {5^{20}}.C_{20}^{20} = {(5 - 1)^{20}} = {4^{20}}\\
S = \frac{{{S_1} - {S_2}}}{2} = \frac{{{6^{20}} - {4^{20}}}}{2}
\end{array}\)
