设{a}是正数数列，其前n项和Sn满足Sn=14（an-1）（an+3）．（1）_爱下问搜题

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问题解答题

设{a}是正数数列，其前n项和S_n满足S_n=

1

4

（a_n-1）（a_n+3）．
（1）求a₁的值；求数列{a_n}的通项公式；
（2）对于数列{b_n}，令b_n=

1

sn

，T_n是数列{b_n}的前n项和，求

lim

n→∞

T_n．

答案

（1）由a₁=S₁=

1

4

(a1-1)(a1+3)，及a_n＞0，得a₁=3

由Sn=

1

4

(an-1)(an+3)得Sn-1=

1

4

(an-1-1)(an-1+3)．

∴当n≥2时，an=

1

4

(

a

2n

-

a

2n-1

)+2(an-an-1)

∴2（a_n+a_n-1）=（a_n+a_n-1）（a_n-a_n-1）∵a_n+a_n-1＞0∴a_n-a_n-1=2，

∴{a_n}是以3为首项，2为公差的等差数列，∴a_n=2n+1

（2）由（1）知S_n=n（n+2）∴bn=

1

Sn

=

1

2

(

1

n

-

1

n+2

)，

T_n=b₁+b₂+…+b_n

=

1

2

(1-

1

3

+

1

2

-

1

4

++

1

n-1

-

1

n+1

+

1

n

-

1

n+2

)

=

1

2

[

3

2

-

2n+3

(n+1)(n+2)

]=

3

4

-

2n+3

2(n+1)(n+2)

∴

lim

n→∞

Tn=

lim

n→∞

[

3

4

-

2n+3

2(n+1)(n+2)

]=

3

4

(13分)

由

an+bn

2

＜0，得a1+(b1-a1)•(

1

2

)n＜0

得

a1+b1

2n

＜-a，得

b1-a1

-a1

＜2n

∴log2

a1-b1

a1

＜n

因而n满足log2

a1-b1

a1

＜n的最小整数（14分）

选择题

----I’d like to go shopping with you, but I have a meeting _______.

　　----If you don’t go, ________.

A．to attend; so do I　　

B．attending; so will I

C．attend; neither will I 　　

D．to attend; nor will I

阅读理解

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                               Title:Career education-lifelong education

Reason for career education	Jobseeking is becoming more and more competitive.
__1__between career education and vocational education	Career education is the instruction with the __2__of helping young people to identify,choose and prepare for a career.It focuses on a person's role in work,leisure,or family life.Vocational education is designed to teach __3__occupational skills.
Basic information about career education	The formal and informal learning__4__in the family,in the community and in schools is __5__in career education. Career education helps students to develop selfunderstanding and then use it to make __6__for their education and working life.
Process of career education	In kindergartens and elementary schools,youngsters learn about different types of work.In junior middle schools,children begin to__7__the occupations and leisure activities.In high schools,students get more specific information about occupations and life styles.Many colleges and universities offer career education by providing counseling programs.Teachers and counselors use__8__ways to provide career education.
9	Not only teachers but also parents are responsible for youngsters' career education.The __10__of classroom study with practical work experience really works.