~ ?yvD ?Dy
?=?
K
K
15
~ ?yvD ?Dy
oé-
%
>
é-?
é[à?? V
é5D??
87í
>Zp
aé?

——
>ê
Baà
Q￥? ?
lb
lb
~ ?yvD ?Dy
R
?
BH?￥

1
A
?
E=H?￥

2
A
LLLL
? ?￥

1
26
×
n
n
A
LL,,,,,
321 n
AAAA
S
~ ?yvD ?Dy
a?jù5
oB-? °? ?￡
W?°p;
2
1
1
=X?B??/￥ié1;
2
1
2
1
2
2
+=X1?=??/￥ié9
LLLL;
2
1
2
1
2
1
2 n
n
Xn +++= L??/￥ié91?
n
n
X
2
1
1?= 1
~ ?yvD ?Dy
=a
￥?l
?l,?1 ?
L,3,2,1 I|GQ
￥B

LL,,,,
21 n
xxx (1)
?1í k
,e?
, ?￥
?
?1
￥[,
n
x ?1Y[ (B?[ ).
 (1):1 }{
n
x,
è ?;,2,,8,4,2 LL
n;,
2
1
,,
8
1
,
4
1
,
2
1
LL
n
}2{
n
}
2
1
{
n
~ ?yvD ?Dy
?i 1.
?"
à
B??
, V ATB
??
à
GQ |
.,,,,
21
LL
n
xxx
1
x
2
x
3
x
4
x
n
x
2.

^?Sf
).(nfx
n
=;,)1(,,1,1,1
1
LL
+

n
})1{(
1?
n;,
)1(
,,
3
4
,
2
1
,2
1
LL
n
n
n?
+
}
)1(
{
1
n
n
n?
+
LLL,333,,33,3 ++++
~ ?yvD ?Dy
.}
)1(
1{
1
H￥M t
]?43
 ∞→
+
n
n
n
?a
￥K
lb
lb
~ ?yvD ?Dy
ù5,
? íK9v
H,
^?íK¤í?
B
??￥
′? ?T
^, ? ?
n
x
n
.1
)1(
1,
1
íK¤í?íK9v
H?
n
xn
n
n
+=
ù5,“íK¤í,i?"
I
1? ?¨
D?y
Y
,
=?1
n
xQ
nn
n
11
)1(
1
=?
YV


U
L￥43,
~ ?yvD ?Dy
,
100
1
ó?,
100
11
<
n
?,100
Ho1 >n
,
100
1
1 <?
n
xμ
,
1000
1
ó?
,1000
Ho1 >n
,
10000
1
1 <?
n
xμ,
10000
1
ó?
,10000
Ho1 >n
,
1000
1
1 <?
n
xμ
,0>εó?
,])
1
[(
Ho1
ε
=> Nn
.1 ? ?μ ε<?
n
x
~ ?yvD ?Dy
?l ?T? ?ió?￥?
ε ?

1
l

9i?
N
P¤? Nn >
H￥B M
n
x
??
T ε<? ax
n
?? ?
*
ü?è
a
^

n
x ￥K
??

n
x
l ?? a
:1
,lim ax
n
n
=
∞→
).( ∞→→ nax
n
?T

àμK,ü
a

^? ?￥,
?i;.1 ￥íK¤íD Y
??
T axax
nn
ε<?
..2 μ1D ?ió?￥?
εN
~ ?yvD ?Dy
x
1
x
2
x
2+N
x
1+N
x
3
x
+3
d,
ε2
ε?a
ε+a
a
.)(
,),(,
 ??àoμoμμK?
=?

μ￥?
H?
N
aaxNn
n
εε +?>
:?lN?ε
?;:
B? ?ó￥?,:à
μB?i?
.,,0,0
lim
ε<?>>?>ε?
=
∞→
axNnN
ax
n
n
n
μ
H
P
~ ?yvD ?Dy
K￥?l?ó pK￥ZE,
è 1,1
)1(
lim
1
=
+
∞→
n
n
n
n
￡
ü
￡
1?
n
x 1
)1(
1
+
=
n
n
n
n
1
=
,0>ε ?ó,1 ε<?
n
x1,
1
ε<
n
o1,
1
ε
>n
[,
],
1
[
ε
=N |,
H5? Nn>
ε<?
+
1
)1(
1
n
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 <=
∞→
qq
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
1a
K￥?é
1aμ??
?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
2a·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
3a0
￥
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 ? OK
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
Bal2
 ù? M
p ;
K K
±Xaú ??la+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
>Zp
——
>ê
Baà
Q￥? ?
~ ?yvD ?Dy
aé?

oé-
%
>
é-?
é[à?? V
é5D??
87í
>Zp
——
>ê
Baà
Q￥? ?
~ ?yvD ?Dy
oé-
%
>
é-?
é[à?? V
é5D??
87í
>Zp
aé?

——
>ê
Baà
Q￥? ?
~ ?yvD ?Dy
oé-
%
>
é-?
é[à?? V
é5D??
87í
>Zp
aé?

——
>ê
Baà
Q￥? ?
~ ?yvD ?Dy
oé-
%
>
é-?
é[à?? V
é5D??
87í
>Zp
aé?

——
>ê
Baà
Q￥? ?
~ ?yvD ?Dy
oé-
%
>
é-?
é[à?? V
é5D??
87í
>Zp
aé?

——
>ê
Baà
Q￥? ?
~ ?yvD ?Dy
oé-
%
>
é-?
é[à?? V
é5D??
87í
>Zp
aé?

——
>ê
Baà
Q￥? ?
~ ?yvD ?Dy
oé-
%
>
é-?
é[à?? V
é5D??
87í
>Zp
aé?

——
>ê
Baà
Q￥? ?
~ ?yvD ?Dy
oé-
%
>
é-?
é[à?? V
é5D??
87í
>Zp
aé?

——
>ê
Baà
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
Ba ?¨
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