Đáp án:
$S = {2^{24}}.$
Giải thích các bước giải:
\(S = C_{25}^{13} + C_{25}^{14} + ...... + C_{25}^{25}\)
Ta có: \(\left\{ \begin{array}{l}C_{25}^0 = C_{25}^{25}\\C_{25}^1 = C_{25}^{24}\\.....\\C_{25}^{12} = C_{25}^{13}\end{array} \right.\)
\(\begin{array}{l} \Rightarrow 2S = 2\left( {C_{25}^{13} + C_{25}^{14} + ...... + C_{25}^{25}} \right)\\ \Leftrightarrow 2S = C_{25}^0 + C_{25}^1 + ...... + C_{25}^{24} + C_{25}^{25}\\ \Leftrightarrow 2S = {\left( {1 + 1} \right)^{25}}\\ \Leftrightarrow 2S = {2^{25}}\\ \Leftrightarrow S = \frac{{{2^{25}}}}{2} = {2^{24}}.\end{array}\)
