问题 填空题
用简便方法计算:
(1+
1
2
+
1
3
+
1
4
)×(
1
2
+
1
3
+
1
4
+
1
5
)
-(1+
1
2
+
1
3
+
1
4
+
1
5
)×(
1
2
+
1
3
+
1
4
)
=______.
答案

1
2
+
1
3
+
1
4
=a,
1
2
+
1
3
+
1
4
+
1
6
=b,则:

(1+

1
2
+
1
3
+
1
4
)×(
1
2
+
1
3
+
1
4
+
1
5
)-(1+
1
2
+
1
3
+
1
4
+
1
5
)×(
1
2
+
1
3
+
1
4
),

=(1+a)×b-(1+b)×a,

=b+ab-a-ab,

=b-a,

=(

1
2
+
1
3
+
1
4
+
1
6
)-(
1
2
+
1
3
+
1
4
),

=

1
6

故答案为:

1
6

阅读理解
单项选择题 A1型题