1/23+303/2323+50505/232323+7070707/23232323+909090909/232323232323-1

1/23+303/2323+50505/232323+7070707/23232323+909090909/232323232323-1
1/23+303/2323+50505/232323+7070707/23232323+909090909/232323232323-1

1/23+303/2323+50505/232323+7070707/23232323+909090909/232323232323-1
1/23+303/2323+50505/232323+7070707/23232323+909090909/232323232323-1
令y＝1/23+303/2323+50505/232323+7070707/23232323+909090909/232323232323-1
303＝101×3,2323＝101×23
50505＝10101×5,232323＝10101×23
7070707＝1010101×7,23232323＝1010101×23
909090909＝101010101×9,2323232323＝101010101×23
故,y＝1/23+3/23+5/23+7/23+9/23－1＝2/23

因为
303＝101×3，2323＝101×23
50505＝10101×5，232323＝10101×23
7070707＝1010101×7，23232323＝1010101×23
909090909＝101010101×9，2323232323＝101010101×23
所以原式＝1/23+3/23+5/23+7/23+9/23－1
＝25/23-1
=2/23