题目内容
(2011•武汉模拟)设S1=1+
+
,S2=1+
+
,S3=1+
+
…,Sn=1+
+
,设S=
+
+…+
,其中n为正整数,则用含n的代数式表示S为( )
1 |
12 |
1 |
22 |
1 |
22 |
1 |
32 |
1 |
32 |
1 |
42 |
1 |
n2 |
1 |
(n+1)2 |
S1 |
S2 |
Sn |
分析:首先求出
,
,..观察第一步的几个计算结果,得出一般规律.
S1 |
S2 |
解答:解:∵
=
=
,
=
=
,
=
=
,
=
=
,…,
猜想:
=1+
-
,
∴S=
+
+…+
=1+1-
+1+
-
+…+1+
-
=n+1-
=
.
故选:B.
S1 |
1+1+
|
3 |
2 |
S2 |
1+
|
7 |
6 |
S3 |
1+
|
13 |
12 |
S4 |
1+
|
21 |
20 |
猜想:
Sn |
1 |
n |
1 |
n+1 |
∴S=
S1 |
S2 |
Sn |
=1+1-
1 |
2 |
1 |
2 |
1 |
3 |
1 |
n |
1 |
n+1 |
=n+1-
1 |
n+1 |
=
n2+2n |
n+1 |
故选:B.
点评:此题考查了数字算式的变化规律.关键是观察几个结果的结果,由特殊到一般,得出规律.
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