问题 解答题
先观察下列计算
1
2
+1
=
2
-1
1
3
+
2
=
3
-
2
1
4
+
3
=
4
-
3
1
5
+
4
=
5
-
4
,…
从计算结果中寻找规律,并据此规律计算:(
1
2
+1
=
1
3
+
2
+
1
4
+
3
+…+
1
2010
+
2009
+
1
2011
+
2010
)(
2011
+1)
答案

根据题意,得

(

1
2
+1
=
1
3
+
2
+
1
4
+
3
+…+
1
2010
+
2009
+
1
2011
+
2010
)(
2011
+1)

=(

2
-1+
3
-
2
+…+
2011
-
2010
)(
2011
+1)

=(

2011
-1)(
2011
+1)

=2011-1

=2010.

(

1
2
+1
=
1
3
+
2
+
1
4
+
3
+…+
1
2010
+
2009
+
1
2011
+
2010
)(
2011
+1)=2010.

判断题
问答题 简答题