To add the numbers \(1,000,000,000,000,000,000\) and \(500,000,000,000,000,000,000\), you can align them by their place values:
\[ \begin{array}{r} 1,000,000,000,000,000,000 \
- 500,000,000,000,000,000,000 \ \hline 501,000,000,000,000,000,000 \ \end{array} \]
Thus, the result of the addition is:
\[ 501,000,000,000,000,000,000 \]