1/42+1/56+1/72+1/90+1/110
来源：学生作业帮助网 编辑：六六作业网 时间：2024/11/24 02:00:31
1/42+1/56+1/72+1/90+1/1101/42+1/56+1/72+1/90+1/1101/42+1/56+1/72+1/90+1/1101/42+1/56+1/72+1/90+1/110
1/42+1/56+1/72+1/90+1/110
1/42+1/56+1/72+1/90+1/110
1/42+1/56+1/72+1/90+1/110
1/42+1/56+1/72+1/90+1/110
=1/（6×7）+1/（7×8）+1/（8×9）+1/（9×10）+1/（10×11）
=1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11
=1/6-1/11
=5/66
（请注意：1/42=1/（6×7）=1/6-1/7,后面方法相同.这是解题的关键）
=1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11=1/6-1/11=1/66