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问题 解答题
对于数列{an}，若存在一个常数M，使得对任意的n∈N*，都有|an|≤M，则称{an}为有界数列．
（Ⅰ）判断an=2+sinn是否为有界数列并说明理由．
（Ⅱ）是否存在正项等比数列{an}，使得{an}的前n项和Sn构成的数列{Sn}是有界数列？若存在，求数列{an}的公比q的取值范围；若不存在，请说明理由．
（Ⅲ）判断数列an=
1
3
+
1
5
+
1
7
+…+
1
2n-1
(n≥2)是否为有界数列，并证明．
答案

（Ⅰ）1≤an=2+sinn≤3，

故{an}为有界数列…（2分）

（Ⅱ）设公比为q，当0＜q＜1时，Sn=

a1(1-qn)
1-q
＜
a1
1-q
，

则正数数列{Sn}满足|Sn|＜

a1
1-q
，即为有界数列；

当q=1时，Sn=na1→+∞，故为无界数列；

当q＞1时，Sn=a1+a2+…+an＞na1→+∞，此时为无界数列．

综上：当且仅当0＜q＜1时，{Sn}为有界数列…（6分）．

（Ⅲ）{an}为无界数列，事实上an=

1
3
+
1
5
+
1
7
+…+
1
2n-1
＞
1
4
+
1
6
+
1
8
+…+
1
2n

∴2an＞

1
3
+
1
4
+
1
5
+
1
6
+…+
1
2n-1
+
1
2n

∴2a2n＞

1
3
+
1
4
+
1
5
+
1
6
+…+
1
2•2n
=(
1
3
+
1
4
)+(
1
5
+
1
6
+
1
7
+
1
8
)+(
1
9
+…+
1
16
)+…+(
1
2n+1
+
1
2n+2
+…+
1
2n+2n
)＞
1
4
×2+
1
8
×4+
1
16
×8+…+
1
2n×2
×2n=
n
2

∴a2n＞

n
4

故当n无限增大时an也无限增大，

所以{an}无界…（12分）．

单项选择题

下面哪项不是初级卫生保健服务（）。

A.健康教育和健康促进

B.疾病预防和保健服务

C.基本治疗

D.专科医疗

E.社区康复
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单项选择题

Right is right. Right7 Of course. But is left wrong Well, the Romans used to think so. They thought left-handed people were mistakes of nature. Latin, the language of the Romans, had many words that expressed this view. Some words we use today still have this meaning. The Latin word "dexter" means "right". The English word "dexterous" comes from this word. It means "handy" (clever with hands). So, right is handy. But the Latin word for left is "sinister". The English word "sinister" comes from this word. Sinister means "evil" (very bad). Is it fair to call right-handed people handy and left-handed people evil Well, fair or not, many languages have words that express such beliefs. In old English, the word for left means "weak". That isn’t much of an improvement over "evil".

Not very long ago, children were often forced to write with their right hands. Doctors have since found that this can be very harmful. You should use the hand you were born to use.

People who use their left hands are just starting to get better treatment. But why they get all these bad names in the first place One reason may be that there are not as many left-handed people as there are right-handed people. There is one left-handed person for every five right-handed ones. People who are different are often thought to be wrong. But attitudes do seem to be changing. Fair-minded right-handed people are finally starting to give left-handed people a hand.

After we read the article we can certainly know that（）

A. left-handed people have been treated poorly

B. the number of the left-handed people is larger than that of the right-handed people

C. right-handed people are much cleverer than left-handed people

D. left-handed people are less smart but hardworking
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