Chapter 1.1A, Problem 7A

Without computing each sum of the arithmetic sequence, find which is greater, $O$ or $E$, and by how much.

$\begin{array}{rll}O& =& 1+3+5+7+\mathrm{...}+97\\ E& =& 2+4+6+8+\mathrm{...}+98\end{array}$