›
›

Tài liệu ôn thi THPT Quốc Gia môn Toán - Chuyên đề 6: Tổ hợp – xác suất – nhị thức Newton

pdf 16 trang Người đăng khoa-nguyen Lượt xem 1164Lượt tải 1 Download
Bạn đang xem tài liệu "Tài liệu ôn thi THPT Quốc Gia môn Toán - Chuyên đề 6: Tổ hợp – xác suất – nhị thức Newton", để tải tài liệu gốc về máy bạn click vào nút DOWNLOAD ở trên
Tài liệu ôn thi THPT Quốc Gia môn Toán - Chuyên đề 6: Tổ hợp – xác suất – nhị thức Newton
	

		 
 !"		!"	
#$%&''&'%%


()	*+	$*,)-.	/	%&001%1 
2345504
	
	




 
 	


 ! ! " " " ! !
  # #  #
	 6 	 6 6 	 	 	 	 	 	 	
6
 7   7     7   7  7  7− − − − −
=
+ = = + + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + +∑ 
 $%&

+ '
  	 7±  !	 + ()*
+(),+-.()+/0()/1
*
())234 6 	 6	 	 
−
= #
+ 5)6+ ! # #
6 	 6 6
	 	   7
−
+ = *
()  2 !6 = − #
+ '
  	 7− 27/89
 8+ : 8− : 8+ ;#;
+ 5)1?()<*
334#
+ @
 A8+
*
3B+ /-3 2(C /?D
BE/-3#FG?
 ! ! ! !H!   " #	 	 	 	 8 	 	 	 	 	 	 	8  8  8    
− =+ = + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + → + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + = 
!
 ! ! !!   !  ! #
8
	 	 	 	 	 	8  8  8    
=−
−
• − = − + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + − ⇒ − + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + − = 
 FE
+*8ID.*
D.?J
@D.*K
+ L
+* M # !# "###N#"#!8  !#	
 	 	 	 	 	= = − − ≥ #
+ FID. ( )M 8  ! #
 M
6
 6 	
	 6
= ≤ ≤
−
#
+ 'D.
M
8 ! 
M# M M
6
6 	
	
 6 	
6 	 6 6
= = ≤ ≤
−
*
 ! !!
6 6 6
	 	 	  
+ +
++ = #

!"#$%&#$' ()*+,-%./0
1 ).23' 4 p q n(ax bx )+ 5670" 7/ .!) k k
n n n
A , C , P . 


 '2<()E%/O$.*K%
P,

!"
!
8  #8 8
8
 
+ ∀ ≠ 
 
 Q5 R"S#  3
T
N
"
!
8
8
 
− ⋅ 
 
 Q5 ! #− 

! 
!
" 8  #8 8
8
 
− ∀ ≠ 
 
 Q5 U VS#−  
!"
N
N
8
8
 
+ ⋅ 
 
 Q5 R"S# 

!"
!
8  #8 8
8
 
+ ∀ > 
 
 Q5 SRT#  W ( )
!U
T
!
" 8  #8 8
8
 
+ > 
 
 Q5 VT"U# 

X
N
S
!
8  #8 8
8
 
+ ∀ > 
 
 Q5 NT#  
!X
S N
N "
!
8 #8 8
8
 
+ ∀ ≠  
 
 Q5 "SN! # 


 '2<(),() 9 *

3@/
()<7
P
 !X" N  #8 :−  U R #9 8 :=  Q5 R U R!XN #" # #− 
3 "T  #8 :+  !" !N #9 8 :=  Q5 !N"T # 
 R N #8 −  S #9 8=  Q5 T TRN # #− 

89:;?@
;	



www.MATHVN.com - Toán Học Việt Nam
 www.DeThiThuDaiHoc.com
	

		 
 !"		!"	
#$%&''&'%%


()	*+	$*,)-.	/	%&001%1 
23455;4
 !!! N  #8−  V #9 8=  Q5 V V!!N # # 
 " !"N  #8 8−  !T #9 8=  Q5 R N!"N # #− 
W " !  "  #8 8−  !V #9 8=  Q5 NNV # 

S 
"
!
8  #8 8
8
 
+ ∀ ≠ 
 
 N!#9 8=  Q5 NS # 

! 
" " 8  #8 8
8
 
− ∀ ≠ 
 
 !!#9 8=  Q5 N N! " # #− 
 N " X  #8 8− +  " #9 8=  Q5 NT# 
Y
! 
8  8  #
8
8: 8: :
:
 
+ ∀ ≥ ≠ 
 
 V " #9 8 :=  Q5 ST# 
 " N T!  #8 8 8+ + +  ! #9 8=  Q5 ! !# 
 T " ! ! "  ! N  #8 8 8 8− + +  T #9 8=  Q5 NN" # 
< S T V X" ! " ! " ! " ! #8 8 8 8+ + + + + + +  T #9 8=  Q5 URV# 


 '2<(),() 	 
P8*K+?JD.(
 
T
!
8  #8 8
8
 
+ ∀ ≠ 
 
 S#	 =  Q5 !" # 
3 !TN  #8−  !N#	 =  Q5 !""UT# 
 
!T
!
8  #8 8
8
 
− ∀ > 
 
 V#	 =  Q5 T!T # 
 "T" N  #8−  "!#	 =  Q5 T " " "T" #N # # 


 '2<(),<O()
-2<<O()/0
 F
()Z?A[<\ N !T #	 	 = '2<()E%

	
, N
S
" !
8  
T
8 8
	 8
 
+ > 
− 
] Q5 SX NT# = 
3 '2<(), S8 
3 N
"
8  8
8 8
8
 
− ∀ ≠ 
 
3@
()^Z[<\
 V "S # STS
	 	 	 
−
−
+ = ] Q5 U_  !XR"#	 = − 
 '2<()/O$.*K%
 N
T "U
!
# 8  8
8 8 8
8
 
+ ∀ ≠  
 
3@4
()^Z
[<\/0 ! " XR	 	 	 	 	  
− −+ + = ] Q5 XR"# 
 F

N !
T
 R XT
8

− +
= *

!
T
!
 N !
TT
8
7
−
− +
= #'2<+()^ 88 3@4() N 

	
 U  7+ 34 ""S # Q5 !  "#8 8= ∨ = 
 '2<++, 88 3@
 T! N   " N" "
8
8− − +  
() V 34 "! 
*
 ! N ""	 	 	  + = # Q5   "8 8= ∨ = #
W F

()Z?A[<\ " " "N " N !T	 	  	+ = + #'2<()
! 8 

	
 N
"
N
" 8  
8 8
8
 
− ∀ ≠ 
 
# Q5 S V S ! ! #" #N # 8 #
 F
 "! "! "  ###
 	8   8  8  8+ = + + + + *K 	
∗∈ #`@4 N "" !S = #
'2<] Q5 V SS	 = #
www.MATHVN.com - Toán Học Việt Nam
 www.DeThiThuDaiHoc.com
	

		 
 !"		!"	
#$%&''&'%%


()	*+	$*,)-.	/	%&001%1 
234554
 '2<()E 8 
 N
"
8  #
8 8
8
 
+ > 
 
`@4 	 [<\/0
 V X U R U "N N "	 	 	 	 	     ++ + + = # Q5
V V
!T #" N" N"  = #
 F
 	 +∈ *
 8  8  # 7 7 > `@
	


7
7
 
+ 
 
a
S R 8 7 2<()b  *
 7 *K()<34] Q5 V VT T 7 #
Y F
 	 
()Z?A[<\ N " ! "! ! N
	 	 	 	   
− +
− − +− = #'2<(),()
!!8 

 N U 8  #
N
	 	
 8 8 8
8
−
 
= − ≠ 
 
 Q5 U U!" #S # 
 F
 	  
 ()Z?A [<\/0 ! "!V !V 
	 	 
−
+ = + #'2<(),
X8  

 N! " " 	8 8− + ] Q5 """S− #
 F
 " N S " !"! " !"!  ## #
 8 8 8   8  8  8= − + − = + + + + '2< X ] Q5 S − #
< '2<(), T8 
 " "! "  ! N  8	 	
 8 8 8 8= − + + 3@4 " !! T
	 	 
−
+− = #
 Q5 NN" # 
 F
 ! !! ! R! " ! !!   !  " ##
 8 8 8 8  8  8  8 = + + = + + + + + #'2< T ] Q5 VX"# 

 F
 ( )
" ! 
N
"
! !
8  #
 8 8 8 8
88
   
= − + − ∀ ≠  
  
5*
cd23(C:<
3
Z()] Q5"R()#
A1 ).23' 4 p q n(a bx cx )+ + 5670" 7/ .!) k k
n n n
A , C , P . 
e@
          # 
	 	 6	< = < = < = < =	 6 	 6 6 6 	 6  6  
	 	 6
6 6 

 8  78 8  78 8   78 8    78 8− − −
= = =
 = + + = + + = + =  ∑ ∑ ∑ 

# #  #  8
	 6
< =6 	 6  6  
	 6
6 
   78 8− −
= =
= ∑∑ *K 8  #6  ∈ 


 '2<(),() 9 *

3@/
()<7
P
 " ! ! N  #8 8+ +  S #9 8=  Q5 !VRT# 
3 " ! ! " N  #8 8+ +  S #9 8=  Q5 U UT# 
 " ! ! "  #8 8+ +  !X #9 8=  Q5 NUS # 
 " T" N  8  #8 8 8+ − ∀ ≥  " #9 8=  Q5 "N #− 
 " T ! #8 8+ −  N #9 8=  Q5 ! #− 
W " N U!  #8 8+ −  U #9 8=  Q5 "NU# 
 " N T!  #8 8 8+ + +  ! #9 8=  Q5 ! !# 
 
!"
S !! 8  #8 8
8
 
− − ∀ ≠ 
 
 U #9 8=  Q5 "X!TR#− 


 '2<(),<O()
-2<<O()/0
 F
 " ! " " ! " " !  8 8   8  8  8+ − = + + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + #'2< U ] Q5 U ST = #
3 F
 ( ) "!   8  #
 8 8 8 8
8
 
= − + ∀ ≠ 
 
f+/()E.gO*
%
 
 8 3@[ N " !"	 	 	  ++ = # Q5 RU#− 
 '2<() S8 
3
!
N ! 8  
8 8
8
  
+ − >  
  
]`@4
()Z
?A[<\ ! " N! " !N U N	 	 	  + + ++ = # Q5 SS"" #
www.MATHVN.com - Toán Học Việt Nam
 www.DeThiThuDaiHoc.com
	

		 
 !"		!"	
#$%&''&'%%


()	*+	$*,)-.	/	%&001%1 
234554
 F
 N " N! " N! " 
 	8 8   8  8  8− + = + + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + #f+/() V 8 3@
4
!T
N! "
" N
!
" "" "
 	
 

 
+ + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + = ⋅ 
 
 Q5 V !T  = − #
 F
 ! " " " !S! " !S! "  N S S  8 8 8   8  8  8+ + + = + + + ⋅ ⋅ ⋅ + #'2< V ] Q5 V SU"SRV = #
W '2<(), ! 8 
	

""
N! # "
S
	8 8 8
 
+ + + 
 
*K
()^Z[
<\/0 N " !S	 	  	
−+ = # Q5 ! "RTV RV = #
B1 ).C (p q n p q n(ax bx ) ; a bx cx )+ + + 567DE + 
h	
 ! ! ! !  8	 	 	 	 	 	 	 	 	 	 7     7  7  7
− − −+ = + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + + *K
 5)1#@
3E()
-
=<2
-334 ! #
 @7,3/2(C   #	 7− 
 '
3 " S ###6 6	 	 	  + + 

i
-

j2/
7$
3  	 7− *
  	 7+ d 8  7 :O

i
-/


j
*@#


 `@+()
 "! 	8+ 
! "S#'2<(), !"8 ] Q5 ! _ "! #	 = 


 '2<(), V8 
 N
!
8
8
8
 
+ 
 
*K
()Z?A*
3@4+
()
34! "S] Q5 ! _ "! #	 = 


 '2<(),() U8 
 ( ) TN"
 8 8
8
 
= + 
 
*K 8 > #`@[<\
/0 ! " ! S RT	 	 	 	 	   
−+ + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + + = # Q5 U S!" #" XR"  = #


 '2<(), ! 8 
 "  8	8+ 3@4
()Z?A[<\
/0 ! ! " " N NN N N N  ! " SU	 	 	 	 	 	 	 	 	 	    
− − −
− + − + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + − = # Q5 ! ! !! #" "" = = #


 '2<(), ! 8 
 " N  8  8	8 8 8− > 3@4
()Z?A*

+()
34 " SU− ] Q5 SSTT#− 


 '2<(), ! 8 
 "  8	8+ 3@4
()Z?A[<\
/0 ( ) ! ! " " N NN N N N ### ! " SU	 	 	 	 	 	 	 	 	    − − −− + − + + − = # Q5 "" #


 '2<  () , !R8  
   3  R" ! # " 8	
 8 8= − +  3@ 4  
 () Z
?A ! " ### " SU	 	 	 	   + + + + = ] Q5 URV #


 '2<(), X8 
/ "" k N  8	8 
/
()Z?A[<\
/0 ! N T " !" ! " ! " ! " ! ! "S
	 	 	 	   
+
+ + + ++ + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + = ] Q5 X " RRT"  = − #


 '2<  () S8  
   "! "  8	8 8+ +  3@  
 () Z ?A [ <\ /0 
 " S "
" " " "### T!"
	 	 	 	   + + + + = # Q5 ! T #


 L\2<(), T8 
 " N  ! " S  	
 8 8 8= − + #
`@4 " S V U ! V T N" !S " !S " !S " !S " !S " !
	    + + + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + = − *K
()Z?A#
Q5 N ! " S N ! T T TT !" N !" S !" T" S U S  " #      = − − + − 


 '2<() !U8 
 !N "   "  " S	
 8 8 8 8= + − + #`@Z?A[<\
/0 ! " " " ! " ! " ! " !
	 	 	  + + ++ + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + = − # Q5 !U !T!NUU!V = #

www.MATHVN.com - Toán Học Việt Nam
 www.DeThiThuDaiHoc.com
	

		 
 !"		!"	
#$%&''&'%%


()	*+	$*,)-.	/	%&001%1 
2345514
F1 
!"#$G0H.% 5).C n(a bx) .+ 
f&	
  	 78+ ()6+ !
6 	 6 6 6
6 	   7 8
−
+ = #
Q- 8  6 	 6 66 	   7 6 	
−
= ≤ ≤ 2\()
{ }6 #h/()K7

[
.?A2 !
!
6 6

6 6
 
6
 
+
−
 ≥
⇒ ≥
<%
  

6 	 6 6
6 	   7
−⇒ = #


 '

!!
! "
N N
8 
+ 
 

 " !!! " !!  8  8  8+ + + ⋅ ⋅ ⋅ + #L\2</() 6 K7*

b]  !!8   Z 6 6≤ ≤  Q5
U
U
<% !!!!
"
#
N6
 = #


 F
 !! "  8
	8   8  8+ = + + ⋅ ⋅ ⋅ + 
/ 	∈ *
+() !8 8###8 	   [<\
 ! S RV" "

 + + ⋅ ⋅ ⋅ + = #'2<()K7
+() !8 8###8 	   ] Q5 <% !"VX" # = 


 F
 " ! "
!
" N
8
  8  8  8
 
+ = + + + ⋅ ⋅ ⋅ + 
 
#'2<()K7
+() ! "8 8 8###8 	    ]
`@4
()^Z[<\ " " " ! ! !" !! "T	 	 	 	 	 	 	 	 	     
− − − −+ + = ] Q5 <%
! !
V"" U
 = ⋅ 


 '2<()Z?A[7 (

  ! 	8+  I()() Z@.

PZ34
X
!T
] Q5 "!	 = #
I1 
!#$' -JK%&#$' G#$ -LM1.% 5).C n(a b) .+ 
f&   	 7+  () 6+ # #
 >
< =6 	 6 6 6
	 	  7 
−
= α β  *K 8 α β  
+()B I#5)
BI12<[<\ ( ) 8  

<
6 6 	 6
>
=

∈

∈ ≤ ≤ ⇒
 ∈




  6 	 6 6
	  7
−⇒ 
()12<#


 '2<()
()Z
 N N " 8	+ 3@4
()Z?A
[<\/0 ( )N " N "X# # #	 	 	 	 	 	
    
= # Q5 N N !R N #" *
 R NR " # 


 '2<()BI

N !
N! T #
"
	+
 
+ 
 
`@4
()Z?A[<\
/0 ! " " N""
	 	 	 	   
− − −
++ + = # Q5
 V N "
! ! " #T_ 
N" N"
 
⋅ 
 %&DE 
1 >N3O  PQR%&DHST  k k
n n n
A , C , P #
• '
  	 7− 27/89
 8+ : 8− : 8+ ;#;
• 5)1?()<*
334#
• e$g
b7 ! !! 8 
6 6 6 6 	 6
	 	 	 	 	    
+ + −
++ = = *

!
!
! !
# #
! !
6 6
	 	 6 	
+
+=+ +
#
• h-.B+b,ED.  # 8?	 	 ⋅ ⋅ ⋅ + + ⋅ ⋅ ⋅ c/?J(
(+
(),3@l3$*K8G(
(+(),()<l3$,
 "! 	8− *K !   ! ######	 	8 8− + 
www.MATHVN.com - Toán Học Việt Nam
 www.DeThiThuDaiHoc.com
	

		 
 !"		!"	
#$%&''&'%%


()	*+	$*,)-.	/	%&001%1 
23455'4


 'b+(
 ! TT T T #@   = + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ +  Q5
T" #@ = 
3 ! " " T TT T T T" " " #@    = + + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ +  Q5
TN #@ = 
 ! ! U UU U US S S #@   = + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ +  Q5
UT #@ = 
 ! " " ! " ! " ! " ! " !  #@    = + + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ +  Q5
" ! " #@ = 
 ! " " " ! " ! " ! " ! " ! " ! " " " #@    = + + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ +  Q5
" ! N #@ = 
W V X U R ! ! ! ! ! ! #@     = + + + +  Q5 NUV#@ = 
 " " S ! ! ! ! ! #@   8  = + + + ⋅ ⋅ ⋅ +  Q5
RR" #@ = 
 ! N N T T " R " R" ! " ! " ! " ! "# " # " # " # #@    = + + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ +  Q5
" ! ! N !#
"
@ = − 


 'b ( ) ( )" !! " ! "" " " "! ! ! !! # ! #" N " !
6 	6 	
	 	 	 	@    6 	
+
−
= − + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + − + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + −
+
 Q5
"
" !
@
=
+
#


 'b
! ! ! !
"M#" !"M SM#" ! M " !"M#"M " !SM
@ = + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + + ⋅  Q5
" !N" !
" !SM
@
−
= #


 L\b+(
 " ! " " " N " " !N! " !N " !N " !N " !N! # " # N # " !N # #@    = + + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ +  Q5
" !!" !N#" !S#" # #
3 
 ! " " !N
" !N " !N " !N " !N
" ! " N " !S
   
@ = + + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + ⋅  Q5
" !S
"
" !
" !S
@
−
= #


 F< " ! " " "     
	 	 	 	   + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + = *K "8 	 	≥ ∈ #


 F
()^Z "8	 ≥ </G
" " " ! !
" "
"
!
! " !  !
	 	 	 	   
+
+
     
−
+ + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + = ⋅          + +     



 'b
!" !" !"!" !"
!N " !N " !S!" !S
!!#!" !!#!" !!#!" " !"#" !N " !N#" !S
   
@ = + + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + + ] Q5 !!" !N
!
!N"
@ = #


 F< "8  8	 	∀ ≥ ∈ E
!
 ! " "###
!
	 	 	   	
−
 
−≤  
− 
#


 '2<()Z?A[<\/G(/m
 " " " " " " " " " " !T !V
" " " " "#N #N #N #N " #" !
6 6 	 	 	 	
	 	 	 	 	    
− −+ + ⋅ ⋅ ⋅ + + ⋅ ⋅ ⋅ + + = + # Q5 U	 = #
A1 ).25670+'%+C %UDE 
)1>N3O +'%H7
•   $  +  ()/ ?K  D. > 1 " " "!8 "8 N8 ###8  ! 8 " 8 ###8  	 	  
-
=<1 " " " 8 ###8 N8 "8 ! 8###8 " 8 ! 	 	  E7#L6+A

 # 6	6  
-
!# 6 	 6 6	6   7
− − #
• n?A.+.=
+ `?K!#f&P ! ! " " " ! ! 	 	 	 	 	 	 	 	 	 	 	 	 8     8   8  8  8
− − − −+ = + + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + + #
+ `?K"#o7/

<*@/?D
  ! ! ! " " ! " !  "  ! #	 	 	 	 	 	 	 	 	 	  8     8 	  8  8
− − − − − −+ = + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + − +    
+ `?KN#Fd+%*
bD.^*
/03
/@*
#


 F< !8  8	 	 ∗∀ ≥ ∈ 2 ! ! " " N N k!#N "# #N N# #N # #S #	 	 	 	 	 	 	 	   	  	
− − −+ + + ⋅ ⋅ ⋅ + = 


 F< !8  8	 	 ∗∀ ≥ ∈ 2 ! ! ! " N N S S !" " " " #N #	 	 	 	 	 	 	 	 	 	    	 	
− − − − −+ + + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + = 


 '2< 8	 +∈ [ ! " " N N S " " !" ! " ! " ! " ! " !"#" N#" S#" " !#" " T
	 	 	 	 	    	 
+
+ + + + +− + − + ⋅ ⋅ ⋅ + + =  Q5 ! "# 


 'b @ 
+?JD.(
www.MATHVN.com - Toán Học Việt Nam
 www.DeThiThuDaiHoc.com
	

		 
 !"		!"	
#$%&''&'%%


()	*+	$*,)-.	/	%&001%1 
23455&4
 " S V ! ! ! ! ! S U !" " #@    = + + + ⋅ ⋅ ⋅ +  Q5
RR! #" #@ = 
3 ! " " " " " " " N " ! #@    = + + + ⋅ ⋅ ⋅ +  Q5
" ! !#" #@ = 
 ! " " V " X" X " X " X " X " X" U " X " V " #@     = + + + ⋅ ⋅ ⋅ + +  Q5
" V" R#" #@ = 


 F
 N
"
"
  8 
 8 8 	
8
∗ 
= − ∈ 
 
 #L\2<() V 88 3@4
() ^Z[<\
/G ! ! " " N N !!#" "#" N#" !"#N	 	 	 	 	 	 	 	   	
− − − −+ + + ⋅ ⋅ ⋅ ⋅ ⋅ + = # Q5 V V V!""  8 #


 F
 ! ! RR "! RU RR !  ! 8  8  8  8  8 − = + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + + + #
'b ! RR " !! RU RR! #" RR #" " #" ! #" !@    = + + ⋅ ⋅ ⋅ ⋅ ⋅ + + + # Q5 " !@ = #


 F
 " !S " " !S! " " !S! N  8   8  8  8− = + + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + #
'b ! ! " !S" N " !T@    = + + + ⋅ ⋅ ⋅ ⋅ ⋅ + ] Q5
" !SN ""#"@ = #


 'b " S " !S" !S " !S " !S " !SN T " !T#@    = + + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + # Q5
" !N! U#"@ = #


 'b+3 " S V " !S" !S " !S " !S " !S" N ! X    = + +

Tài liệu đính kèm:

  • pdfChuyen de 6. To hop, xac suat, nhi thuc Newotn.pdf