内容正文:
书书书
… +(2n-3 ()· )12
n
+(2n-1 ()· )12
n+1
,
!"#$%&'(
1
2
Rn =1·
1
2
+ [ (2 )12
2
(
+
)12
3
+… (+ )12 ]
n
-(2n-1 ()· )12
n+1
=1
2
+2·
(14 1- 12n- )1
1-1
2
-(2n-1 ()· )12
n+1
,
)*'(
Rn =3-(2n+3 ()· )12
n
,
+
(2n+3 ()· )12
n
>0,
'(
c1+c2+…+cn<3.
21.
!
:(1)
,-.(
b1 =a2 =6,
/01
{an}2345267401,89 a1 =4,
89
an =4+2(n-1)=2n+2.
:5
b1+
b2
2
+
b3
3
+… +
bn-1
n-1
+
bn
n
=an+1,
89
b1+
b2
2
+
b3
3
+… +
bn-1
n-1
=an(n≥2),
#$%&(
:
bn
n
=an+1-an =2,n≥2,
89
bn =2n,n≥2,
/
b1 =6;<=!$,89 bn =
6, n=1,
2n,n≥2{ .
(2)
>
n≥ 2?,
1
anbn
= 1
(2n+2)(2n)
=
1
4n(n+1)
= (14 1n- 1n+ )1 ,
89
Sn =
1
a1b1
+ 1
a2b2
+ 1
a3b3
+… + 1
anbn
= 1
4×6
+ [14 12-( )13 (+ 13- )14
+… (+ 1n- 1n+ ) ]1
= 1
24
+1
4
1
2
- 1
n+( )1
= 1
24
+ n-1
8(n+1)
= 2n-1
12(n+1)
,
/>
n=1
?
,S1 =
1
a1b1
= 1
4×6
=1
24<=!$
,
8901
1
anb
{ }
n
6@
n
AB
Sn=
2n-1
12(n+1)
(n∈N+).
22.
!
:(1)
C7D01
{an}63D5 q(q>1),
E+-.F
a1q+a1q
2+a1q
3 =28,
a1q+a1q
3 =2(a1q
2+2{ ),
)*(
2q2-5q+2=0,
G(
q=2
H
q=1
2
(
!
"
).
89
a1 =2,q=2,I an =2
n.
(2)
+
(1)
'F
1
an
= 1
2n
(n∈N+),
+
1
2n
=
b1
2+1
-
b2
22+1
+
b3
23+1
-… +(-1)n+1
bn
2n+1
(n∈N+),
(
1
2n-1
=
b1
2+1
-
b2
22+1
+
b3
23+1
-… +(-1)n
bn-1
2n-1+1
(n≥2),
I
1
2n
- 1
2n-1
=(-1)n+1
bn
2n+1
,
J
bn =(-1) (n 12n + )1 (n≥2),
>
n=1
?
,
1
a1
=
b1
2+1
,
J
b1 =
3
2
,
89
bn =
3
2
, n=1,
(-1) (n 12n + )1 ,n≥2,n∈N+{ .
(3)
:5
cn =2
n+λbn,
89>
n≥3?,cn =2
n+(-1) (n 12n + )1 λ,
cn-1 =2
n-1+(-1)n- (1 12n-1+ )1 λ,
+-.(
cn-cn-1 =2
n-1+(-1)n (λ 2+32 )n >0,
J
(-1)nλ>-
2n-1
3
2n
+2
,
① >n5KLH7L46M0?,
Nλ>-
2n-1
3
2n
+2
OPQ
,
/
2n-1
3
2n
+2
= 1
3
22n-1
+ 1
2n-2
R
n
SKTSK
,
E
n=4
? (, 2
n-1
3
2n
+
)
2 min
=128
35
,
I λ>-
128
35
;
② > n5KLH7L36U0?,
N λ<
2n-1
3
2n
+2
OPQ
,
E>
n=3
? (, 2
n-1
3
2n
+
)
2 min
=32
19
,
I λ<
32
19
;
/>
n=2
?
,
+
cn-cn-1=c2-c1 (= 22+54 )λ
(- 2+32 )λ >0,( λ<8,
V!'(
,
8W λ (6XYZ[2 -12835,32)19 .
"#$%&'()*
(
+
)
,-./01#23
4
、
567
BBBDBD BACDDD
89
:
1.
+\]^_'F`a b c d e f g h ^ X
1500
1200+900+1500
×720=300
i
.
2.P(X=3)=C (36 )12 (
3
1- )12
3
= 5
16
.
3.5
ijcklmklnNijoN#pqr
:
①2,2,1,②3,1,1,
sL ①:tjuklv5wwBx