问题 解答题
先观察下列的计算,再完成:
(1)
1
2
+1
=
(
2
-1)
(
2
+1)(
2
-1)
=
2
-1

1
3
+
2
=
(
3
-
2
)
(
3
+
2
)(3-
2
)
=
3
-
2

1
4
+
3
=
(
4
-
3
)
(
4
+
3
)(
4
-
3
)
=
4
-
3

请你直接写出下面的结果:
1
5
+
4
=______;
1
6
+
5
=______;
(2)根据你的猜想、归纳,运用规律计算:
(
1
2
+1
+
1
3
+
2
+
1
4
+
3
+
+
1
2012
+
2011
)×(
2012
+1)
答案

(1)

1
5
+
4
=
5
-
4
(
5
+
4
)(
5
-
4
)
=
5
-2;
1
6
+
5
=
6
-
5
(
6
+
5
)(
6
-
5
)
=
6
-
5

(2)根据题意得:原式=

2
-1+
3
-
2
+…+
2012
-
2011
=
2012
-1=2
503
-1.

故答案为:(1)

5
-2;
6
-
5

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