问题 解答题
阅读下面问题:
1
1+
2
=
1×(
2
-1)
(
2
+1)(
2
-1)
=
2
-1
1
3
+
2
=
3
-
2
(
3
+
2
)(
3
-
2
)
=
3
-
2
1
5
+2
=
5
-2
(
5
+2)(
5
-2)
=
5
-2

试求:(1)
1
n+1
+
n
=______.
(2)利用上面所揭示的规律计算:(
1
1+
2
+
1
2
+
3
+
1
3
+
4
+…+
1
2012
+
2013
+
1
2013
+
2014
)×(
2014
+1
答案

(1)

1
n+1
+
n
=
n+1
-
n
(
n+1
+
n
)(
n+1
-
n
)
=
n+1
-
n

故答案为:

n+1
-
n

(2)(

1
1+
2
+
1
2
+
3
+
1
3
+
4
+…+
1
2012
+
2013
+
1
2013
+
2014
)×(
2014
+1),

=(

2
-1+
3
-
2
+
4
-
3
+…+
2013
-
2012
+
2014
-
2013
)×(
2014
+1),

=(

2014
-1)×(
2014
+1),

=2014-1,

=2013.

单项选择题
单项选择题