问题 解答题
计算:(
1
2
+1
+
1
3
+
2
+
1
4
+
3
+…+
1
2009
+
2008
)(
2009
+1)
答案

(

1
2
+1
+
1
3
+
2
+
1
4
+
3
+…+
1
2009
+
2008
)(
2009
+1)

=(

2
-1+
3
-
2
+…+
2009
-
2008
)(
2009
+1)

=(

2009
+1)(
2009
-1

=2009-1

=2008.

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