搜题请搜索小程序“爱下问搜题”
问题 解答题

在数列{an}中，a1=2，an+1=4an-3n+1，n∈N*．

（1）证明数列{an-n}是等比数列；

（2）设数列{an}的前n项和Sn，求Sn+1-4Sn的最大值．

答案

（1）由题设an+1=4an-3n+1，得an+1-（n+1）=4（an-n），n∈N*．

又a1-1=1，

所以数列{an-n}是首项为1，且公比为4的等比数列．

（2）由（Ⅰ）可知an-n=4n-1，

于是数列{an}的通项公式为an=4n-1+n．

所以数列{an}的前n项和Sn=

4n-1
3
+
n(n+1)
2
，Sn+1=
4n+1-1
3
+
(n+2)(n+1)
2

所以Sn+1-4Sn=-

1
2
（3n2+n-4），

故n=1，最大值为：0．

单项选择题

室内装修费科目不包括( )。

A．材料费、工器具、设备使用费

B．人工费、管理费、承包商利润

C．材料费、工器具、承包商利润

D．健身设备、游泳池和其他康乐设施的维修、保养和日常使用费等
查看答案
阅读理解

“It is one of the few bright spots in the Chinese economy，” says Zeng Ming. He is talking about e­commerce. Mr. Zeng, the chief strategy officer for Alibaba, a giant Chinese Internet firm, predicts that digital transactions on his firm's platforms will top 1 trillion yuan($159 billion) this year—more than Amazon's and eBay's combined. That is a bold claim, but consider what happened on Singles Day.

Invented a few years ago by students and seized upon by digital marketers, this festival for lonely hearts falls annually on the 11th day of the 11th month(since 1 is the loneliest number). It is like St Valentine's Day, only worse. Singletons show each other with tender gifts: a barrage of pearls; a storm of sweets.

This November 11th they spent a surprising 19 billion yuan on Alibaba's online platforms—a fourfold increase on a year ago, and more than double what Americans spent online last Cyber Monday(the Monday after Thanksgiving, when retailers urge Americans to shop online). About 100 million purchases were logged, accounting for 80% of the packages shipped that day. Couriers(快递员) were buried in parcels.

So life is good for China's e­tailers. Then? Not exactly. The number of digital marketers is increasing and online sales are booming. Consumers are enjoying lower prices, better service and more variety. The problem? The pressure on profits in Chinese e­commerce is worse than in America, reckons Elinor Leung of CLSA, a broker. “Almost no one makes money，” she says.

The fiercest battles are being fought between online retailers and their bricks­and­mortar(实体的) rivals. Dangdang, a firm that resembles Amazon, and 360buy, another online retailer, have cut prices fiercely. Tencent, a cash­rich online giant known for its instant­messaging software, is splashing out to win market share. 360buy has also just raised $400 millon from investors to do the same. But it is unclear how much longer such firms can burn through capital.

小题1:What's the best title of this passage?

A．The Ambition of Alibaba

B．Fierce Competition between Retailers

C．A New Festival for the Singles

D．Chinese Booming E­commerce小题2:According to Zeng Ming, this year Alibaba will ________.

A．outweigh Amazon and eBay in worldwide influence

B．rank top among all the Internet firms

C．have more than 159 billion dollars' sale

D．create another sales miracle just like the one on Singles Day小题3:How many packages were shipped on November 11th from Alibaba's online platforms?

A．About 80 million.

B．About 100 million.

C．About 125 million.

D．About 180 million.小题4:What's the author's attitude towards online retailers in China?

A．Optimistic.

B．Concerned.

C．Sympathetic.

D．Indifferent.
查看答案