题目内容
阅读理解:
=
-
,
=
-
…
=
-
阅读以上信息,完成下列问题:
(1)
+
+
=
;(填最后结果)
(2)
+
+
+
=
;(填最后结果)
(3)求
+
+…+
的值.
1 |
1×2 |
1 |
1 |
1 |
2 |
1 |
2×3 |
1 |
2 |
1 |
3 |
1 |
x(x+1) |
1 |
x |
1 |
x+1 |
阅读以上信息,完成下列问题:
(1)
1 |
1×2 |
1 |
2×3 |
1 |
3×4 |
3 |
4 |
3 |
4 |
(2)
1 |
x(x+1) |
1 |
(x+1)(x+2) |
1 |
(x+2)(x+3) |
1 |
(x+3)(x+4) |
3 |
x(x+3) |
3 |
x(x+3) |
(3)求
1 |
1×2 |
1 |
2×3 |
1 |
x(x+1) |
分析:(1)根据题中所给的例子进行计算即可;
(2)、(3)根据题中所给的例子找出规律,再根据此规律进行计算.
(2)、(3)根据题中所给的例子找出规律,再根据此规律进行计算.
解答:解:(1)∵
=
-
,
=
-
,…
=
-
∴原式=1-
+
-
+
-
=1-
=
.
故答案为:
;
(2)∵
=
-
,
∴原式=
-
+
-
+
-
=
-
=
;
(3)∵
=
-
,
=
-
,
…
=
-
,
∴原式=1-
+
-
+…+
-
=1-
=
.
1 |
1×2 |
1 |
1 |
1 |
2 |
1 |
2×3 |
1 |
2 |
1 |
3 |
1 |
x(x+1) |
1 |
x |
1 |
x+1 |
∴原式=1-
1 |
2 |
1 |
2 |
1 |
3 |
1 |
3 |
1 |
4 |
1 |
4 |
3 |
4 |
故答案为:
3 |
4 |
(2)∵
1 |
x(x+1) |
1 |
x |
1 |
x+1 |
∴原式=
1 |
x |
1 |
x+1 |
1 |
x+1 |
1 |
x+2 |
1 |
x+2 |
1 |
x+3 |
1 |
x |
1 |
x+3 |
3 |
x(x+3) |
(3)∵
1 |
1×2 |
1 |
1 |
1 |
2 |
1 |
2×3 |
1 |
2 |
1 |
3 |
…
1 |
x(x+1) |
1 |
x |
1 |
x+1 |
∴原式=1-
1 |
2 |
1 |
2 |
1 |
3 |
1 |
x |
1 |
x+1 |
1 |
x+1 |
x |
x+1 |
点评:本题考查的是分式的加减,根据题意找出规律是解答此题的关键.
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