$解:(3) 原式 = \frac {1}{2} × (\frac {1}{2}-\frac {1}{4}+\frac {1}{4}-\frac {1}{6}+\frac {1}{6}- \frac {1}{8}+···+\frac {1}{2022}-\frac {1}{2024})$
$=\frac {1}{2} × (\frac {1}{2}-\frac {1}{2024})$
$=\frac {1}{2} ×\frac {1011}{2024}$
$=\frac {1011}{4048}$