问题 解答题
先阅读下列材料,再解答后面的问题.
1
1×3
=
1
2
(1-
1
3
)
1
3×5
=
1
2
(
1
3
-
1
5
)
1
5×7
=
1
2
(
1
5
-
1
7
)
,…,
1
17×19
=
1
2
(
1
17
-
1
19
)

1
1×3
+
1
3×5
+
1
5×7
+…+
1
17×19

=
1
2
(1-
1
3
)+
1
2
(
1
3
-
1
5
)+
1
2
(
1
5
-
1
7
)+…+
1
2
(
1
17
-
1
19
)

=
1
2
(1-
1
3
+
1
3
-
1
5
+
1
5
-
1
7
+…+
1
17
-
1
19
)

=
1
2
(1-
1
19
)=
9
19

(1)在和式
1
1×3
+
1
3×5
+
1
5×7
+
…中,第五项为______,第n项为______;
(2)计算
1
(x-1)x
+
1
x(x+1)
+
1
(x+1)(x+2)
+
1
(x+2)(x+3)
答案

(1)在和式

1
1×3
+
1
3×5
+
1
5×7
中,

第五项为:

1
9×11

第n项为:

1
(2n-1)(2n+1)

(2)

1
(x-1)x
+
1
x(x+1)
+
1
(x+1)(x+2)
+
1
(x+2)(x+3)

=

1
x-1
-
1
x
+
1
x
-
1
x+1
+
1
x+1
-
1
x+2
+
1
x+2
-
1
x+3

=

1
x-1
-
1
x+3

=

x+3-x+1
(x-1)(x+3)

=

4
(x-1)(x+3)

单项选择题
单项选择题