问题 解答题
观察下列分母有理化的运算.
1
2
+1
=
2
-1,
1
2
+
3
=
3
-
2
1
3
+
4
=
4
-
3

1
2005
+
2006
=
2006
-
2005
1
2006
+
2007
=
2007
-
2006

利用上面的规律计算:
1
2
+1
+
1
2
+
3
+
1
3
+
4
+…+
1
2005
+
2006
+
1
2006
+
2007
)(1+
2007
答案

1
2
+1
+
1
2
+
3
+
1
3
+
4
+…+
1
2005
+
2006
+
1
2006
+
2007
)(1+
2007

=(

2
-1+
3
-
2
+
3
-
2
+…+
2007
-
2006
)(1+
2007

=(

2007
-1)(1+
2007

=2007-1

=2006.

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