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
答
原式=
×(1-1 2
+1 3
-1 3
+1 5
-1 5
+…+1 7
-1 2009
+1 2011
-1 2011
)1 2013
=
×(1-1 2
)1 2013
=
×1 2
2012 2013
=
.1006 2013