问题 选择题
已知数列{log2(an-1)}(n∈N*)为等差数列,且a1=3,a2=5,则
lim
n→∞
1
a2-a1
+
1
a3-a2
+…+
1
an+1-an
)=(  )
A.2B.
3
2
C.1D.
1
2
答案

数列{log2(an-1)}(n∈N*)为等差数列,

设其公差为d,则log2(an-1)-log2(an-1-1)=d,

an-1
an-1-1
=2d,又由a1=3,a2=5,

则d=1,即

an-1
an-1-1
=2,

{an-1}是以a1-1=2为首项,公比为2的等比数列,

进而可得,an-1=2n,则an=2n+1,

故an-an-1=2n-2n-1=2n-1

lim
n→∞
1
a2-a1
+
1
a3-a2
+…+
1
an+1-an
)=
lim
n→∞
1
2
+
1
4
+…+
1
2n-1
)=1,

故选C.

阅读理解
阅读理解。
       You are travelling in Inner Mongolia. You want to book a room in a hotel, but you don't know
any hotels. Look at the following two pages from a brochure (小册子). Then answer the questions.
I                                       
Happy Holiday Hotel                     
150 rooms                               
Two restaurants (24 hr.)                
Swimming pool                           
Near the downtown 189 Shanghai Road     
Double room:¥30/day (without bathroom) 
Single room:¥60 / day                  
Tel: 0778-7404475            
Fax: 0778-8808865                       
Whether you are a large or small group,
we are happy to help you!      
       II                                  
Grassland Hotel    
Beautiful scenery in all seasons            
Great for large groups of families    
A restaurant with delicious food    
Outdoor sports available                   
Double room:¥40 / day (with bathroom)  
Single room:¥50 / day    
Tel: 0858-3893493    
Fax: 0858-3883593                          
You can enjoy yourselves by riding
horses and eating delicious food!
1. Where is the Happy Holiday Hotel?   
     ______________________________
2. How much will you pay if you want a double room for two days at the Grassland Hotel?   
     ______________________________
3. How long are the restaurants at Happy Holiday Hotel open for?   
     ______________________________
4. Where should you stay if you want to ride a horse?   
     ______________________________
5. Why are the double rooms more expensive at the Grassland Hotel?
     ______________________________
判断题