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n
n
üμ
.1
)1(
lim
1
=
+
∞→
n
n
n
n
'
?i
~ ?yvD ?Dy
è 2
.lim),( CxCCx
n
n
n
=≡
∞→
￡
ü1è
!
￡
Cx
n
CC?=,? ?ε<
,0>ε ?ó
[,
0=
,n?B M1 ?
.lim Cx
n
n
=
∞→
a
ü,è
￥ K??]Bè
,
l2,¨?l￡
Ki
H,1o
^ ?ió
?ùsN,??A1 pKl￥ N.
,0>ε
~ ?yvD ?Dy
è 3
.1,0lim <=
∞→
n
n
?￡
ü
￡
,0>ε ?ó
,0 ε<=?
n
n
qx,lnln ε<qn
],
ln
ln
[
q
N
ε
= |
,
H5? Nn>
,0 ε<?
n
qüμ,0lim =∴
∞→
n
n
q
,0=q ? ;00limlim ==
∞→∞→ n
n
n
q5
,10 << q ?
,
ln
ln
q
n
ε
>∴
~ ?yvD ?Dy
è 4
.lim
,0lim,0
ax
axx
n
n
n
n
n
=
>=>
∞→
∞→
p￡
O
!
￡,0>ε ?ó
.lim ax
n
n
=
∞→
#
,lim ax
n
n
=
∞→
Q
,
1
ε<?>?∴ axNnN
n
Hμ
P¤?
ax
ax
ax
n
n
n
+
=?V7μ
a
ax
n
<
a
1
ε
< ε=
~ ?yvD ?Dy
1 a
K￥?é
1 aμ??
?l,
n
x, ?i ?
M,
P¤B M1
?
n,μ Mx
n
≤ ? ?,5?
n
x μ?,
?5,?1í?,
è ?,;
1+
=
n
n
x
n
.2
n
n
x =
à
??μ?
￥?
n
x ?
> uW
],[ MM?
,
μ?
í?
~ ?yvD ?Dy
? ?
l ?￥
A?μ?
￡
,lim ax
n
n
=
∞→
!
??l,,1=ε |
,1,<?>? axNnN
n
Hμ
P¤?5
.11 +<<? axa
n
'μ
},1,1,,,max{
1
+?= aaxxM
N
L:
,,Mxn
n
≤￥μ5B M1 ?
{ },μ?#
n
x
?i μ??
^
l ?￥A1Hq,
w
í?
A?? ?
~ ?yvD ?Dy
2 a·B?
? ?
?
l ?￥
oμB? K
￡
,lim,lim bxax
n
n
n
n
==
∞→∞→
?
!
??l,
P¤.,,0
21
NN?>ε?;
1
ε<?> axNn
n
Hμ?;
2
ε<?> bxNn
n
Hμ?
{ },,max
21
NNN = |
Hμ5? Nn> )()( axbxba
nn
=?
axbx
nn
+?≤
.2ε=ε+ε<
.
H?
? ?
T?? ba =
#
l ?
K·B,
~ ?yvD ?Dy
è 5
.)1(
1
^? ?￥￡
ü
+
=
n
n
x
￡
,lim ax
n
n
=
∞→
!
??l,,
2
1
=ε?
,
2
1
,,? ?μ
H
P¤?5 <?>? axNnN
n
),
2
1
,
2
1
(,+?∈> aaxNn
n
H'?
uWé1 1.
,1,1
?
í¨?1Qˉ |7?
n
x
? V
]
Hê? é1 1￥ uW
=,
.,}{,? ?? ?
^μ?￥
Y
L
n
x
~ ?yvD ?Dy
3 a0
￥
l ??
{ }
{}
{}￥0
0
￥B?
?1e
??￥5aQ??"¤?t[ e
?? ?i |íK [i?l
n
n
n
x
x
x
LLL,,,,,
21 ni
xxxx
LL,,,,
21 k
nnn
xxx
{ }
{},knnxx
kxx
kknn
nn
k
kk
≥[A ?? ?
^? e
7
[
^??B?[ 0
?i
è ?
~ ?yvD ?Dy
? ?
l ?
￥ ?B0
9
l ? O K
M]
￡
{ } { }￥ ?B0
^
!
nn
xx
k
,lim ax
n
n
=
∞→
Q
.,,0,0 εε <?>>?>?∴ axNnN
n
μ
H
P
,NK = |
,
H5? Kk >
.Nnnn
NKk
≥=>
.ε<?∴ ax
k
n
.lim ax
k
n
k
=∴
∞→
￡8
~ ?yvD ?Dy
? a
K￥
15
bayxyx
n
n
n
n
nn
n
±=±=±
∞→∞→∞→
limlim)(lim
abyxyx
n
n
n
n
nn
n
=?=
∞→∞→∞→
limlim)(lim
b
a
y
x
y
x
n
n
n
n
n
n
n
==
∞→
∞→
∞→
lim
lim
lim
ax
n
n
=
∞→
lim by
n
n
=
∞→
lim
? ?
! 5
(1)
(3)
(2)
?
H
0≠b
~ ?yvD ?Dy
B al2
ù? M
p ;
K K
±X aú ??l a+il ;
l ?
￥?é
μ?? a·B? a0
￥
l ??,
~ ?yvD ?Dy
± I5
·/
￡
ü 1lim =
∞→
n
n
n ?￥p
￡
ü 1
P
,1 ε+<
n
n
o1
P )1ln(ln
1
ε+<n
n
V7?
2ln
)1ln(
ln
)1ln(1 εε +
<
+
<
nn
¤
,0>?ε
|
1
)1ln(
2ln
+
+
=
ε
N
?
HAμ ? ?Nn> ε+<< 10
n
n
1lim =∴
∞→
n
n
n
~ ?yvD ?Dy
± I53s
ε+<1
n
nQ
)1ln(ln
1
ε+<n
n
~
?N
￡
ü?
?¨￥
2ln
)1ln(
ln
)1ln(1 εε +
<
+
<
nn
L=
ü
^??
T
)1ln(
ln2ln
ε+<<
n
n
n
'￡
ü?
àμ?¨ o
a?bv p￥′
n
nln
~ ?yvD ?Dy
V7
H
2ln
)1ln( ε+
>> Nn
?μ ? ?
)1ln(
2ln
ε+<
n
??
^ ￥ sHq
)1ln(
ln
ε+<
n
n
Q7
êl1
n
2ln
~ ?yvD ?Dy
aé?
oé-
%
>
é-?
é[à?? V
é5D??
87í
>Z p
——
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Q￥? ?
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oé-
%
>
é-?
é[à?? V
é5D??
87í
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——
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%
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é-?
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%
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%
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é5D??
87í
>Z p
aé?
——
>ê
B aà
Q￥? ?
~ ?yvD ?Dy
.}
)1(
1{
1
H￥M t
]?43
∞→
+
n
n
n
? a
￥ K
~ ?yvD ?Dy
.}
)1(
1{
1
H￥M t
]?43
∞→
+
n
n
n
? a
￥ K
~ ?yvD ?Dy
.}
)1(
1{
1
H￥M t
]?43
∞→
+
n
n
n
? a
￥ K
~ ?yvD ?Dy
.}
)1(
1{
1
H￥M t
]?43
∞→
+
n
n
n
? a
￥ K
~ ?yvD ?Dy
.}
)1(
1{
1
H￥M t
]?43
∞→
+
n
n
n
? a
￥ K
~ ?yvD ?Dy
.}
)1(
1{
1
H￥M t
]?43
∞→
+
n
n
n
? a
￥ K
~ ?yvD ?Dy
.}
)1(
1{
1
H￥M t
]?43
∞→
+
n
n
n
? a
￥ K
~ ?yvD ?Dy
.}
)1(
1{
1
H￥M t
]?43
∞→
+
n
n
n
? a
￥ K
~ ?yvD ?Dy
.}
)1(
1{
1
H￥M t
]?43
∞→
+
n
n
n
? a
￥ K
~ ?yvD ?Dy
.}
)1(
1{
1
H￥M t
]?43
∞→
+
n
n
n
? a
￥ K
~ ?yvD ?Dy
.}
)1(
1{
1
H￥M t
]?43
∞→
+
n
n
n
? a
￥ K
~ ?yvD ?Dy
.}
)1(
1{
1
H￥M t
]?43
∞→
+
n
n
n
? a
￥ K
~ ?yvD ?Dy
.}
)1(
1{
1
H￥M t
]?43
∞→
+
n
n
n
? a
￥ K
~ ?yvD ?Dy
B a ?¨
K￥?l￡
ü
a
2
3
12
13
lim =
+
+
∞→
n
n
n
a 19....999.0lim =
∞→n
= a
!
n
x μ?? 0lim =
∞→
n
n
y
￡
ü 0lim =
∞→
nn
n
yx
5
