题目内容

计算:
1
1×2010
+
1
2×2009
+…+
1
2010×1
-
2010
2011
(
1
1×2009
+
1
2×2008
+…+
1
2009×1
)

=______.
1
1×2010
+
1
2×2009
+…+
1
2010×1
-
2010
2011
(
1
1×2009
+
1
2×2008
+…+
1
2009×1
)

=
1
2011
1
1
+
1
2010
+
1
2
+
1
2009
+…+
1
2010
+
1
1
)-
2010
2011
×
1
2010
1
1
+
1
2009
+
1
2
+
1
2008
+…+
1
2009
+
1
1

=
1
2011
1
1
+
1
2010
+
1
2
+
1
2009
+…+
1
2010
+
1
1
-
1
1
-
1
2009
-
1
2
-
1
2008
-…-
1
2009
-
1
1

=
1
2011
1
2010
+
1
2010

=
1
2011
×
1
1005

=
1
2021055

故答案为:
1
2021055
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