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
7
+
6
的值;
(2)
1
n+1
+
n
(n为正整数)的值.
(3)计算:
1
1+
2
+
1
2
+
3
+
1
3
+
4
+…+
1
98
+
99
+
1
99
+
100
答案

(1)

1
7
+
6
=
7
-
6
(
7
+
6
)(
7
-
6
)

=

7
-
6
7-6

=

7
-
6

(2)

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

=

n+1
-
n
n+1-n

=

n+1
-
n

(3)原式=

2
-1+
3
-
2
+
4
-
3
+…+
99
-
98
+
100
-
99

=

100
-1=10-1=9.

单项选择题 A1/A2型题
单项选择题