计算:1/1×3+1/3×5+…+1/2009×2011+1/2011×2013.

问题描述:

计算:

1
1×3
+
1
3×5
+…+
1
2009×2011
+
1
2011×2013

原式=

1
2
×(1-
1
3
+
1
3
-
1
5
+
1
5
-
1
7
+…+
1
2009
-
1
2011
+
1
2011
-
1
2013

=
1
2
×(1-
1
2013

=
1
2
×
2012
2013

=
1006
2013