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高三数学数列专题练习及答案



5 60 1 2, 5,2 2, 11,..., 2 5 ( A) 6 ( B) 7 (C ) 10 2 {an } 5 S5 25 a2 3 a7

( D) 11

( A) 12
3

( B) 13

(C ) 14 ( B) . y sin x, x R 1 ( D) . y ( ) x , x R 2

( D) 15

3

( A) y x , x R (C ) . y x, x R
4 a n a n

1 n n 1 (C ) 120
n

n 10 n



( A) 11

( B) 99
n

( D) 121
( C)
n 1

5 an a 1 a 1 a 4 an

2 ( B) 4 3 3 6 x ( ,0) sin x , tan 2 x = 2 5 7 7 ( A) ( B) . 24 24

3 ( A) 4 2

3 (C ) 4 2

n 1

2 ( D) 4 3
(

)

(C ) .

24 7

( D)

24 7

7 4 40 4 80 210 D18 ( A) 12 ( B) 14 (C ) 16 8 1, (1 2), (1 2 2 ), , (1 2 2 2
2 2 n1

), n S n Sn




n

(C ) 2 n1 n ( D) 2 n1 n 2 1 9 {an } a1 2 an 1 an ln(1 ) an n ( A) 2 ln n ( B) 2 (n 1) ln n (C ) 2 n ln n ( D) 1 n ln n ( A) 2 ( B) 2 n n
10 y

3 sin x cos x x [
( B) . 2



, ] 2 2
(C ) .
3





( A) 1

( D) .

3 2

11{an}{bn} n S n Tn

a S n 5n 3 5 b5 Tn 2n 7
( D)
48 25

( A)

28 17
2

( B)
2

23 15

(C )

53 27

12. 1, 2cos , 2 cos

, 23 cos3 ,L L , 100 0
( B) . 2k



( A) . k


3

(k Z )


3

(k Z )

(C ) . 2k

2 (k Z ) 3

( D) .


5 20 13 {an } a1a3 a2 a4 2a2 a3 49 a2 a3

14 f ( x) cos( 3x )(0 ) f ( x) f ' ( x) _________ 15 n y x n (1 x) x2 y a n

an n n 1
16 an log( n1) (n 2) nN* a1 a2 L ak kkN*" " [12008] 10 20

17 l n : y x 2n Cn : x 2 y 2 2an n 2(n N ) AnBn, {an } a1 1, an 1 {an } bn

1 2 An Bn . 4

n (an 2), {bn } n S n . 3

18 an d n S n , S4 2S2 4 , bn 1 d 5 2 a1 bn 2 3 n N * bn b8 a1

1 an an


5 60

BBACC

DBDAB

DC

5 60 13 7

10 20 17 1 d

14 6

15 Sn

2 1 2n 1 2

2n 1 2

162026

n

1 An Bn )2 2an 2, an 1 2 2(an 2) 2 an 3 2n 1 2 n bn (an 2) n 2n 1 , 3 0 1 2 n 1 2 S n 1 2 2 2 3 2 n 2 an 1 (
2Sn 1 21 2 22 3 23 n 2n
Sn (n 1)2n 1 18 1 S4 2S2 4 4a1 d 1

3 4 d 2(2a1 d ) 4 2

5 7 2 a1 an an a1 (n 1) n 2 2
bn 1

1 1 1 7 an n 2

f ( x) 1

1 7 x 2

7 7 , , 2 2

b3 b2 b1 1 n 4 1 bn b4 bn b4 3 b3 1 2 bn 1

1 1 bn 1 an n a1 1 1 ,1 a1 1 a1 , x a1 1

f ( x) 1

x 1 a1 y 1 x 1 a1 y 1 .

n N * bn b8 7 1 a1 8 7 a1 6 a1 (7, 6)


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