问题 解答题
阅读下面解题过程:
1
2
+1
=
1-(
2
-1)
(
2
+1)(
2
-1)
=
2
-1
(
2
)
2
-12
=
2
-1
2-1
=
2
-1
1
3
+
2
=
1-(
3
-
2
)
(
3
+
2
)(
3
-
2
)
=
3
-
2
(
3
)
2
-(
2
)
2
=
3
-
2
3-2
=
3
-
2

请回答下列问题:
(1)仿照上面格式写出
1
4
+
3
的变形过程;
(2)直接写出
1
n
+
n-1
的结果;
(3)化简
1
1+
2
+
1
2
+
3
+
1
3
+
4
+
1
98
+
99
+
1
99
+
100
答案

(1)原式=

4
-
3
(
4
+
3
)(
4
-
3
)
=
4
-
3
=2-
3

(2)

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

(3)原式=

2
-1+
3
-
2
+
4
-
3
+…+
99
-
98
+
100
-
99
=10-1=9.

单项选择题
单项选择题