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Tài liệu Luyện thi đại học - Phần đại số tổ hợp ppt

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./-
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0
4
5
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4
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3211
322

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1
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M

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

 –!!–!"!"#$%&'


( ) ( )
( ) ( )
3
2
22
33
2
3
3
4
+
−−
=
−−+
−−+
==
+
+















MM
M
MM
M


( ) ( )
( ) ( )
2
1
11
22
1
2
2
3
+
−−
=
−−+
−−+
==
+
+















MM
M
MM
M


3
2
1
1
1
1
1
1
1
1
1
3
4
1

2
+
−−
+
+
+

+
=
+
+
+









 O
( )
1
22
1
42
1
3
1

1
+
+
+
+
+
=
+
+
+
+
+









e F'-
( )
1
22
2
1
1
2
1

2
2
1
+
+
=
+
−−
+
=
+








2
3
3
4
1
2
1
1





+
=
+
+
+



,
,




",_-
32
2
42
3
21
1
2






+

=
+
+
+
U'V
  !"#"$-
1
1
1 +
+
+
=+








4 7.29R-
1
2
11
2
+
+
−+
=++











8
!,'<-
( ) ( )












 +++=++=
−+−+
111
2



.! 

1
21
1
1
+
++
+
+
===







U'V
4 7.29R-
 Y0Z
≤≤=+++
+
−−− 











3
321
33 
8
!,'<-
321
33
−−−
+++=











( ) ( ) ( )
32211
2
−−−−−
+++++=
















2
1
1
11
2

+

++
++=










2
1
1
1
1
11

+

+

++
++=



















3
1
22
+

++
=+=
U'V
4 7%.29R-

3
3
2
2
321
452
+
+
+
+
+++
+=+++















8
–


 –!!–!"!"#$%&'
!,'<-
321
452
+++
+++=












( ) ( )
32211
32
+++++
+++++=















3
1
2
1
1
1
32
+
+

+
+
+
+
++=









( )
3
1
2
1
2
1
1
1
2
+
+
+
+
+
+

+
+
+++=











3
2
2
2
2
+
+
+
+
+=








( )
3
2
2
2
2
2
+
+
+
+
+
+
++=









3
3
2
2
+
+

+
+
+=





U'V
4 7&.
 ≤≤4
(.29R-














4
4321
454
+

−−−−
=++++

8
!,'<-
4321
454
−−−−
++++=













( ) ( )
4332211
33
−−−−−−+
+++++++=


















3
1
2
1
1
11
33

+

+

++
+++=












( )
3
1
2
1
2
1
1
1
1
12
2

+

+

+

+


++
+++++=




















4
1
32
2
+

++
=+=

U'V
4 7'.
 ≤≤1
(.29R-

1
1
11
2
1
1


−−



++++=











((( 

8
!36'7-








1
1
1



==

 







1
1
1




−=

l-






















−=
−=
−=

+

−−





1
1
21
2
2
1
1
1
((((((((((((((((((((((((((((((

.&0@30@''H2'9>,'-












 −=+++
−−



12
2
1
1
((( 

1
1
12
2
1
1


−−



++++=











 (((
U'V
 UC
1
1
1
==







V
4 7(.A=E''D>0E8b

≤≤5
(.29R











5
55
5
11
5
0
5 +
−−
=+++ (((
 UV
8
 5'i-
!,'<-
55
5
11
5
0
5
−−
+++=







 ((( 
–


 –!!–!"!"#$%&'

54321
510105
−−−−−
+++++=












 

( ) ( ) ( )
544332211
464
−−−−−−−−−
+++++++++=
























4
1
3
1
2
1
1
11

464

+

+

+

++
++++=










 

( ) ( )
4
1
3
1
3
1
2

1
2
1
1
1
1
11
33

+

+

+

+

+

+

++
++−++++=

















 

3
2
2
2
1
22
33

+

+

++
+++=












( )
3
2
2
2
2
2
1
2
1
22
2

+

+

+

+

++
+++++=













 

2
3
1
33
2

+

++
++=






 


2
3
1
3
1
33

+

+

++
+++=



















5
1
44 +

++
=+= U'V
 / !"#+23++:$;<=
!,'<-
( )
55
5
44
5
33
5
22
5
1
5
0
5
5
1  +++++=+


( )
((((((
332211

1
−−−−−−
+++=+












( ) ( ) ( )
(((((( ++=+=++
+
+




5
55
111

";T

9,9Q

( ) ( )

 ++ 11
5
=E-

55
5
44
5
33
5
22
5
11
5
0
5
−−−−−
+++++













 
.k;T

9,9Q
( ) ( )

 ++
+
11
5
'o'6=E;T

9,9Q
( )
5
1
+
+


p<$_9,'
4 79'29R-









1
0
++
=
+
=


8
!36'7-







1
1
1 −


+= 









+

+++
+=

1
1


1
1

++++
−=






 
 








+++
=
+
++++=

(((
2
2
1
1
0
0

!,'<-

1
1
2
3
3
4
3
3
1
2
2
3
2

2
0
1
1
2
1
1
0
1
0

++++
+++
+++
+++
+
−=
−=
−=
−=
=
















((((((((((((((((((((((((((((((







1
2
2
1
1
0
+++++
=++++ ((( ,_







1

0
++
=
+
=

U'V
–


 –!!–!"!"#$%&'
 %
P,9Q&Q$2'F',Q$2'R,''',$(S,$<
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 ( F' 5
&-
( )
2


 
4 7.29R-



















6
66
6
55
6
44
6
33
6
22
6
11
6
0
6 +

−−−−−−
=++++++ 
8
!,'<-
( )
66
6
55
6
44
6
33
6
22
6
1
6
0
6
6
1
 ++++++=+


( )
(((((( ++++++++++
−−−−−−−−−−−− 665544332211
1
















 
";T

9,9Q
( ) ( )

 ++ 11
6
=E-
 
66
6
55
6
44
6
33

6
22
6
11
6
6
0
−−−−−−
++++++
k
n
k
n
k
n
k
n
k
n
k
n
k
n
CCCCCCCCCCCCCC

e F'-

( ) ( ) ( )
......111
6

66
++=+=++
+
+
kk
n
nn
xCxxx

";T

9,9Q
( ) ( )

 ++ 11
6
'o'6=E;T

9,9Q
( )
6
1
+
+
n
x
)]$8'2
4 7'29R-

( ) ( ) ( )

n
n
n
nnn
CCCC
2
22
1
2
0
... =+++ 
8
!,'<-
( ) ( ) ( )
nnn
xxx ++=+ 111
2


( )( )
nn
nnnn
nn
nnnn
xCxCxCCxCxCxCC
++++++++= ......
22102210


( )( )

n
n
n
n
n
n
n
n
nn
nnnn
CxCxCxCxCxCxCC ++++++++=
−−
......
221102210

";'G,T

96'
( ) ( )
nn
xx
++ 11
=E-
( ) ( ) ( )
22
1
2
0
...
n

nnn
CCC +++ 
e F'-
( )
nn
n
nn
nnnn
n
xCxCxCxCCx
22
22
22
2
1
2
0
2
2
......1
++++++=+ 
;'G,T

9
( )
n
x+1 =E
n
n
C

2

e E;'G,T

96'
( ) ( )
nn
xx ++ 11 'o'6=E;'G,T

9,9Q-
( )
n
x
2
1 + 

( ) ( ) ( )
n
n
n
nnn
CCCC
2
22
1
2
0
... =+++

U'V

4 7%'29R-

( ) ( ) ( ) ( )
( )
n
n
n
n
nnnn
CCxCxCC
2
2
2
2
2
22
2
2
1
2
2
0
2
1... −=+−+− 
8
!,'<-
( )
nn
n
nn

nnn
n
xCxCxCCx
22
22
1
2
0
2
2
......1
+++++=+ 

( ) ( )
nn
n
n
n
n
nn
n
xCCxCCx
22
22
1
2
0
2
2
...1...1

+±−++−=−

";-T

96'
( ) ( )
nn
xx
22
11 −+
=E-

×