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題目列表(包括答案和解析)

求數(shù)列
1
1+
2
1
2
+
3
,…,
1
n
+
n+1
,…
的前n項和
 

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14、求數(shù)列{(-1)n•n}的前2010項的和S2010

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求數(shù)列2,4,8,16,…前十項的和.

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求數(shù)列1
1
2
,2
1
4
,3
1
8
,4
1
16
,…
前n項的和.

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求數(shù)列的前n項和:1+1,
1
a
+4,
1
a2
+7,…,
1
an-1
+3n-2,…

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一.選擇題

1―5  CBABA   6―10  CADDA

二.填空題

11.       12.()       13.2          14.         15.

16.(1,4)

三.解答題

數(shù)學(xué)理數(shù)學(xué)理17,解:①         =2(1,0)                      (2分)             

        ?,                                        (4分)

?

        cos              =

 

        由,  ,    即B=              (6分)

                                               (7分)

                                                        (9分)

,                                                         (11分)

的取值范圍是(,1                                                      (13分)

18.解:①設(shè)雙曲線方程為:  ()                                 (1分)

由橢圓,求得兩焦點,                                           (3分)

,又為一條漸近線

, 解得:                                                     (5分)

                                                    (6分)

②設(shè),則                                                      (7分)

      

?                             (9分)

,  ?              (10分)

                                                (11分)

  ?

?                                        (13分)

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      單減區(qū)間為[]        (6分)

     

    ②(i)當(dāng)                                                      (8分)

    (ii)當(dāng),

    ,  (),

    則有                                                                     (10分)

    ,

                                                   (11分)

      在(0,1]上單調(diào)遞減                     (12分)

                                                     (13分)

    20.解:①       

                                                            (2分)

    從而數(shù)列{}是首項為1,公差為C的等差數(shù)列

      即                                (4分)

     

       即………………※              (6分)

    當(dāng)n=1時,由※得:c<0                                                    (7分)

    當(dāng)n=2時,由※得:                                                 (8分)

    當(dāng)n=3時,由※得:                                                 (9分)

    當(dāng)

        (

                                              (11分)

                             (12分)

    綜上分析可知,滿足條件的實數(shù)c不存在.                                    (13分)

    21.解:①設(shè)過A作拋物線的切線斜率為K,則切線方程:

                                                                    (2分)

        即

                                                                                                       (3分)

    ②設(shè)   又

         

                                                             (4分)

    同理可得 

                                                    (5分)

    又兩切點交于  ,

                                   (6分)

    ③由  可得:

     

                                                    (8分)

                      (9分)

     

    當(dāng) 

    當(dāng) 

                                                         (11分)

    當(dāng)且僅當(dāng),取 “=”,此時

                                           (12分)

    22.①證明:由,    

      即證

      ()                                    (1分)

    當(dāng)  

          即:                          (3分)

      ()    

    當(dāng)   

       

                                                             (6分)

    ②由      

    數(shù)列

                                                  (8分)

    由①可知, 

                        (10分)

    由錯位相減法得:                                       (11分)

                                        (12分)

     

     


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