题目内容
观察下列分母有理化的计算:
=
-1;
=
-
;
=2-
…,
从计算结果中找出规律,并利用这一规律计算:
+
+
+…+
=
1 | ||
|
2 |
1 | ||||
|
3 |
2 |
1 | ||
2+
|
3 |
从计算结果中找出规律,并利用这一规律计算:
1 | ||
1+
|
1 | ||||
|
1 | ||
|
1 | ||||
|
2
-1
501 |
2
-1
.501 |
分析:首先观察归纳,可得规律:
=
-
,然后将:
+
+
+…+
化为
-1+
-
+2-
+…+
-
,即可求得答案.
1 | ||||
|
n+1 |
n |
1 | ||
1+
|
1 | ||||
|
1 | ||
|
1 | ||||
|
2 |
3 |
2 |
3 |
2004 |
2003 |
解答:解:
+
+
+…+
=
-1+
-
+2-
+…+
-
=
-1
=2
-1.
故答案为:2
-1.
1 | ||
1+
|
1 | ||||
|
1 | ||
|
1 | ||||
|
=
2 |
3 |
2 |
3 |
2004 |
2003 |
=
2004 |
=2
501 |
故答案为:2
501 |
点评:此题考查了分母有理化的知识.此题属于规律性题目,难度适中,注意找到规律:
=
-
实际此题的关键.
1 | ||||
|
n+1 |
n |
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