1/3×5+1/5×7+1/7×9+…1/199×201

来源:学生作业帮助网 编辑:六六作业网 时间:2025/01/25 03:38:02
1/3×5+1/5×7+1/7×9+…1/199×2011/3×5+1/5×7+1/7×9+…1/199×2011/3×5+1/5×7+1/7×9+…1/199×2011/3×5=(1/3-1/5)/

1/3×5+1/5×7+1/7×9+…1/199×201
1/3×5+1/5×7+1/7×9+…1/199×201

1/3×5+1/5×7+1/7×9+…1/199×201
1/3×5=(1/3-1/5)/2
1/5×7=(1/5-1/7)/2
.
1/199×201=(1/199-1/201)/2
原式=(1/3-1/5+1/5-1/7+1/7.+1/199-1/201)/2
=(1/3-1/201)/2
=11/67