问题 选择题

设数列{an}前n项和Sn=Aqn+B,则A+B=0是使{an}成为公比不等于1的等比数列的(  )

A.充分不必要条件

B.必要不充分条件

C.充要条件

D.即不充分也不必要条件

答案

(1)已知{an}成为公比不等于1的等比数列,则

Sn=

a 1(1-q n)
1-q
=
a 1
1-q
-
a 1q n
1-q
,比照Sn=Aqn+B,得

A=

a 1
1-q
,B=-
a 1
1-q

故A+B=0,

(2)若已知:数列{an}前n项和Sn=Aqn+B,A+B=0,则

a1=S1=Aq+B=A(q-1),

n>1时 an=Sn-Sn-1=aAqn+B-[Aqn-1+B]=Aqn-1(q-1),

⇒{an}成为公比不等于1的等比数列.

故A+B=0是使{an}成为公比不等于1的等比数列的充要条件.

故选C.

单项选择题
填空题

A good translator is by definition bilingual. The opposite is not ______(1) true, however. A born and bred bilingual will still need two__________(2) to become a translator: first, the skills and experience necessary for__________(3); second, knowledge of the field in which he or she will__________(4). The skills and experience for translation include the ability to write ______(5) in the target language, the ability to read and understand the_________(6) language material thoroughly, and the ability to work with the latest__________(7) and communication hardware and software.Does a born and bred bilingual__________(8) a better translator than someone who learned language B later in__________(9) There is no definite answer, but the following issues are important.__________(10), a born and bred bilingual often suffers from not truly knowing __________(11) language well enough to translate, with some even suffering from what __________(12) known as a lingualism, a state in which a person lacks_________(13) full, fluent command of any language. Second, born and bred bilinguals__________(14) don’’t know the culture of the target language well enough to_________(15) top-quality translations, or cannot recognize what aspects of the source language__________(16) its culture need to be treated with particular care, as they_________(17) in a sense too close to the language. And last, they often_________(18) the analytical linguistic skills to work through a sticky text.On_________(19) other hand, the acquired bilingual may not have the same in-depth _________(20) of colloquialisms, slang, and dialect that the born bilingual has. Also, the acquired bilingual will not be able to translate as readily in both directions (from B to language A and A to language B). Finally, born bilinguals often have a greater appreciation of the subtleties and nuances of both their languages than someone who learns their B language later in life can ever hope to have.