解：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 {1012-1}{2024} $?
?$=\frac {1011}{4048}$?
