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问题 解答题
已知数列{an}满足a1=2a，an=2a-
a2
an-1
（n≥2），其中a是不为0的常数，令bn=
1
an-a
．
（1）求证：数列{bn}是等差数列；
（2）求数列{an}的通项公式．
答案

∵（1）an=2a-

a2
an-1
（n≥2），

∴bn=

1
an-a
=
1
a-
a2
an-1
=
an-1
a(an-1-a)
（n≥2），

∴bn-bn-1=

an-1
a(an-1-a)
-
1
an-1-a
=
1
a
（n≥2），

∴数列{bn}是公差为

1
a
的等差数列．

（2）∵b1=

1
a1-a
=
1
a
，

故由（1）得：bn=

1
a
+（n-1）×
1
a
=
n
a
．

即：

1
an-a
=
n
a
，

得：an=a（1+

1
n
）．

多项选择题

下列哪些诗篇出自于郭沫若的《女神》？（）

A.《梅花树下的醉歌》

B.《天狗》

C.《我是个偶像崇拜者》

D.《立在地球变上放号》
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单项选择题

Just how does a person arrive at an idea of the kind of person that he is He develops this (1) of self through a gradual and complicated (2) which continues throughout life. The notion is an (3) that one establishes only with the help of others. (4) the elementary knowledge that one is short or tall is a comparative judgment that we cannot make (5) we have the opportunity to (6) ourselves with others. One’s idea of qualities which are harder to (7) is even more dependent upon other people’s ideas.

Whether one is intelligent, or stupid; attractive, or ugly; these and many other ideas of the self are (8) from the reactions of people with whom we (9) This process of (10) the nature of the self from the reaction of others has been labeled the "Looking-glass Self" by Cooley, who carefully analyzed this psychological (11) of self-discovery.

Just as the picture in the mirror gives an image of the physical self, (12) the perception of the reactions of others gives an image of the social self. We know, (13) , that we are good at certain things and not at others. This (14) came to us from the reactions of other persons, first our parents and then other individuals (15) in life. It should be remembered that, as other people’s reactions could be (16) and understood in more than one way, the looking-glass self with which the individual (17) may easily differ from the image others have actually formed of his (18) Clearly, it is our perception of the responses of others and not their (19) responses that (20) our self-image, and these perceptions are often not accurate.

12（）

A.while

B.for

C.so

D.since
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