问题 解答题
数列{an}的前n项和Sn=n(2n-1)an,并且a1=
1
3

(1)求数列{an}的通项公式.
(2)判断前n项和Sn组成的新数列{Sn}的单调性,并给出相应的证明.
答案

(1)当n≥2时,an=Sn-Sn-1=n(2n-1)an-(n-1)(2n-3)an-1,得

an
an-1
=
2n-3
2n+1
a2
a1
a3
a2
a4
a3
a5
a4
an-1
an-2
an
an-1
=
1
5
×
3
7
×
5
9
×
7
11
2n-5
2n-1
×
2n-3
2n+1

a1=

1
3
an=
1
(2n-1)(2n+1)

(2)因为Sn=n(2n-1)an=

n
2n+1
Sn+1-Sn=
n+1
2n+3
-
n
2n+1
=
1
(2n+1)(2n+3)
>0
对于任意的正整数都成立,所以Sn+1>Sn,即前n项和Sn组成的新数列{Sn}为递增数列.

阅读理解

阅读短文,选择正确答案。

     Do you know how to write an English letter? When we write a letter in Chinese, we always put the date at

the end of the letter. But it is different in English. We have to put it on the top of the right corner. And above the

date, we also write the number of our house and the names of our street, city and country. To begin the letter,

we always use words like "Dear sir", "Dear Mr. / Miss / Mrs.…" At the end of the letter, we usually use words

like "Yours" "Yours ever" or "Truly yours". It is also different to write an English envelope (信封). If to an

American friend Jane Shute, write your name and address on the top of the left corner and write hers in the

middle. Now read the following envelope, please.

Qin Ling                                                        

No.11 Middle School                                  STAMP       

Zibo, Shandong, P.R.C. Miss

Jane Shute 65

King Street, New Town

Sydney, Australia

1. "We have to put it on the top of the right corner," The word "it" here means _____. [ ]

A. the date

B. the letter

C. the envelope

D. the passage

2. From the passage, we know when we write an English letter, we should put down our address            . [ ]

A. at the end of the letter on the left

B. at the end of the letter on the right

C. at the top of the letter on the left

D. at the top of the letter on the right

3. How do you begin your letter if you write to Peter White? [ ]

A. Peter

B. Mr. Peter

C. Dear Mr. White

D. Dear Sir Peter

4. To what country will the letter be sent? [ ]

A. P.R.C.

B. America

C. Australia

D. Sydney

5. Who writes this letter? _______. [ ]

A. Zibo

B. Qin Ling

C. MISS Shute

D. Miss Jane

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