What is the sum of all the odd integers between 300 and \(600\)?

The smallest odd integer is \(301\), and the largest one is \(599\). There are \(150\)numbers in this series, so the sum is \(150 \times 450 = \color{brown}\boxed{67,500}\)

Between 300 and 600 - 150 odd integers.

\( \displaystyle\sum_{n=1}^{150} \mbox{ } ( 2n + 299 ) = 67500\), as BB said.