题目内容
阅读下面问题:1 | ||
1+
|
1×(
| ||||
(
|
2 |
1 | ||||
|
| ||||||||
(
|
3 |
2 |
1 | ||
|
| ||||
(
|
5 |
试求:(1)
1 | ||||
|
(2)利用上面所揭示的规律计算:
1 | ||
1+
|
1 | ||||
|
1 | ||||
|
1 | ||||
|
1 | ||||
|
分析:(1)上叙问题中,几个分母的有理化因式互为倒数,
+
的有理化因式为
-
,且(
+
)(
-
)=1;
(2)先分母有理化,再观察抵消规律.
n+1 |
n |
n+1 |
n |
n+1 |
n |
n+1 |
n |
(2)先分母有理化,再观察抵消规律.
解答:解:(1)
=
-
;
(2)
+
+
+…+
+
=
-1+
-
+
-
+…+
-
+
-
=
-1.
1 | ||||
|
n+1 |
n |
(2)
1 | ||
1+
|
1 | ||||
|
1 | ||||
|
1 | ||||
|
1 | ||||
|
=
2 |
3 |
2 |
4 |
3 |
2009 |
2008 |
2010 |
2009 |
=
2010 |
点评:本题考查了分母的有理化因式的确定方法及算式的抵消规律.
练习册系列答案
相关题目