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

–    –!!–!"!"#$%&'           ()*+,- ./- "0* ! (1*2'1345  ( ) ? n a b+ =   ( ) ? n a b− =  !6'7- k k n n n C C − =   1 1 1 1 k k n n n C C k + + + = +  1 1 1 k k k n n n C C C + + + + =     8 5 9  : 7 5 9  : "; 5 9  '< => ?$, @ k nn k n C ,P ,A         .AAB  CD,0EF'9'G,H2'A'I,'J''''8,$- .'-CK'L2''58,$-  ( ) M M B     − = N  OMN ( ) MM M      − =     !"#"$- 1 1 1 + + + =+          % P,9Q&Q$2'F',Q$2'R,''',$(S,$< 7; 1#-0@9'G,H2'=E6''G,,      ( F' 5 &- ( ) 2      &CK,9Q ( ) n bxa + N ( ) n bxa 2 + (S,$<'J,AAT6' 1#EQ'J''8D,0E''=,$- (@9'G,H2''2, 0 n C 0E n n C UF' 0 2n C 0E n n C 2 2 VWX;'G, =EA<,,9Q ( ) ( ) nn x 2 x1 ;1 ++ (S,$<'JTO@$0@9'G,H2' L7$NF'TO@$'<7$ (@9'G,H2''2, 0 n C 0E n n C UF' 0 2 n C 0E n n C 2 2 VWX;'G, =E,   ,'J,9Q ( ) ( ) nn x 2 x1 ;1 ++ (S,$'J ax ±=  Y(@9'G,H2''2, 0 n C 0E n n C UF' 0 2n C 0E n n C 2 2 VWX;'G, '2, kkn ba −  ,'J,9Q ( ) ( ) nn xa 2 xa ; ++ F' ( ) ( ) nn bxa 2 bxa ; ++ A,'- –    –!!–!"!"#$%&'  'J ( ) ( )     T,0Z T,0Z +±= +±= 1  [(1@$EL'<F'99>,\6'9,0]  'CKE'7A'7 V.'Z'8-  ^-.J*2'134Q,9Q  ^-%W_E'7A'7`0@'G,,9Q  ^Y-.J,AAT6' V1#F'9'G,EQ'J''8*2'- ,(a@9'G,H2'7 0   F'     ( )   .F' 0 2  W9 X  A ;0Z<F'8]$50* ,KE'7 (a@9'G,H2'7 0   F'     ( )   .F' 0 2  W9 X   ;0Z<=E6',$_>=>@ ,KE'7 '(a;''JI*2'134R''D,0EF'9'G,''[A,$ b=c''F'9'G,E YV.Id-e &E','<fF'9E,8\6'Q,0]E '<F'99Z8  ( )*+, V.'Z'8-  ^  -.J ,9Q*2'134  ^  -%7_6'\,0@0Z'#6'  ^ Y -66'\,0@ @?$8 V1#F'9'G,EQ'J''8  ,(a@9'G,H2''<'2, 0   0E    UF'   .0E 0 2  VWg$ 9XF'8&50*  (ae X;9'<-   −− − ,'J'#6'\=E      '(a .J I * 2' 134 D, 0E '' [A ,$  b =  '' F' 9'G,6'\  %*-./0     h#Ti- (a!6&Q$2''<'2,    ,_'2&H2''<'2,     ,$( (aSD',$j,'I=E`A@9Z''@?$8U2'=E]$8 '2VA'k`Y',@9Z''@?$8( Y(a @''#F'9'G,EQ'J''8''F' 9'G, C6l>'I,'/]'#@Y''8`E_=E''[A'' m0E''n`(  &P,9Q*2'134U,^V  NU,^TV  (S,$<'J,AAT6' –    –!!–!"!"#$%&'  C[-! &F';'G,( 5- @;2'34Z?$- ( ) 1 0 n n k n k n k a b C a b − = + =   !6o'G,T0E_ CD,0E8@Q6(!p<$_9,F';'  Cm-! ;=Z79,9Q( 5- P,9Q*2'34Z?$( )F k a =E;?$'G,9,9Q Ti65;$'G,b_ { } k a (!p<Q$_9, ( ) max k a  .Id-QTi65;$'G, { } k a 0Z k N∈ ,ql- • Tir- 1 k k a a +  • si;$- 1 k k a a + −                         –    –!!–!"!"#$%&'                       8 5 9  : 7 5 9  : "; 5 9  '< => ?$, @ k nn k n C ,P ,A  123++-!@E3''Z',$- 4 25)F]$;'<+,=E-    ∈ ≥ Nkn kn ,  4 25-CK'''L2',$Q9IJ-  ( ) n k n P. ! ! A kn n − = O !n A ( ) !! ! C k n knk n − =  4 25S,$9IJ'59 :759 :;59 b '0]59 :759 :;59 '58(8 ;0E 'J;6'`]$;`Z' 4 25&P@=$#  6)0Z;59 ,'<Q835Ftl 4 7 8''59 ,$ ,V 13 5 nn CC =  V 1 14 2 1414 2 ++ =+ nnn CCC  8 ,V]$;- Znn ∈≥ ,0  –    –!!–!"!"#$%&'  ( ) ( ) ( )( ) 3012-n !1 ! 5 !3-n3! n! 5 13 =−⇔ − =⇔= n n n CC nn   ( )    = = ⇔=−−⇔ =[ u   0283   #_;'G,59 =EOu V]$;-    ∈ ≤ ⇔    ∈ +≥ ++ v     214       UhV !,'<- 1 14 2 1414 2 ++ =+     ( ) ( ) ( ) ( ) ( ) MM M MM M M[M [M   −+ = −+ +⇔ 131 14 2 122 14   ( )( ) ( )( ) ( )( )  −+ = ++ + − ⇔ 131 2 21 1 14Y     ( )( ) ( )( ) ( )( )  −+=−−+++⇔ 142214132      = = ⇔=+−⇔ 8 03212    [   8UhV #_;'G,59 =E-    = = 8 4    4 7 8''59  ,V   B 43 2 1 =+ +    V ( ) 2 32 1 4     BB =−− +    8 ,V]$;-    ∈ ≥ +   2  !,'<-    B 43 2 1 =+ +    ( ) ( ) ( ) M M MM M Y 2 42 12 − =+ − + ⇔       ( ) ( )  184 −=++⇔ Y   ( ) ( )    = = ⇔=−⇔ # = m  3 2 015     V]$;-    ∈ ≥ +   2   8@ ( ) ( ) ( ) ( ) ( ) 2 3 12 2 4 212       − =− − − − + ⇔ M M M M MM M          ( ) ( ) [[   Y = + ⇔ 2   0310 2 =−+⇔  Y   –    –!!–!"!"#$%&'     =−+ = ⇔ 03108 0 2    59 E_0L; 2≥∀   #_59 b'0L; 4 7'"b_ $_>58bH2'  0 4 5 3 1 4 1 =−− −−   B    8 ]$;-    ≥ ∈ 5    59 b'550Z-  ( ) ( ) ( ) ( ) ( ) ( ) 0 4 2 4 5 43 1 54 1 = − − − − − − − − M M ( MM M MM M         ( ) 0 4 1 4 5 46 1 = − − − − −⇔   [     ( )( ) ( ) 065414 =−−−−⇔ (    0229 =−−⇔      ( )    −= = ⇔ =  2 11    ⇔ O=E9*'  4 78! A ∈ v ^ @- 355 1 11 1 1 ---- = − ++ + +         8 !,'<- ( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 1 1 1 1 + −+ = −+ + −+ + = + + +             MM M MM M  E- ( ) ( ) ( ) ( ) ( )             2 21 1 1 1 1 1 1 +− = +−− + −+ + = − + + MM M MM M  !p8@          = +− = + −+ 3 52 1 1 1      ⇔     =+− = 0683 2    ⇔  + ∈    = =    3 6  #_    = = 6 3   =E''9*'  4 78''59 ,$- ,V      10 3 2 2 1 ≥ +  –    –!!–!"!"#$%&' V ( ) 114 1 1 3 +<+ − ++    B  8 ,V]$;-    ∈ ≥ +   2   ( ) ( ) ( ) MM M ( MM M  2210 3 12 1 10 3 2 2 1 − ≥ − + ⇔≥ +             ( ) 501013 2 1 10 3 2 1 2 ≤≤⇔≤−−⇔ − ≥ +   Y  Y M  C    ∈ ≥ +   2 >OwAYA[Amx #_'';'G,759 =E-OwAYA[Amx V]$;-    ∈ ≥ +   2   ( ) ( ) ( ) ( ) ( ) ( ) 114 21 1 2 114 1 1 3 +< − + + − + ⇔+<+ − ++        MM M M M B    ( )  14 2 1 <+−   ⇔  40282 2 <<⇔<−−   u   C + ∈  0E 2≥ >OwAYx #_'';'G,759 =E-OwAYx 4 7%8''759 ,$- ,V ( )  [ M B 4 143 4 < + +  UV V 24 23 4 ≤ − − +    Y  [  B B  UV 8 ,V]$;- ∈ 1  UV ⇔ ( ) ( ) M MM M 2 4 1434 +< +     ⇔  ( )( ) 143434 <++    ⇔  095284 2 <−+   ⇔ y(mz  z(m C  ∈ > { } A{A=   #_'';'G,759 =E- { } YAA=   V]$;-    ∈ ≥ +   4   UV ⇔ ( ) ( ) ( ) ( ) 24 23 442 1 4 ≤       − − − + − MM M M M M M        –    –!!–!"!"#$%&'  ⇔  ( )( ) 24 23 1 3 4 4 ≤ − − +   M M  ⇔  0564 2 ≤+−   ⇔  51 ≤≤   C    ∈ ≥ +   4 > { } mA4=  #_'';'G,759 =E- { } mA4=   4 7&8759 - 4 5 3 1 4 1 −− −−   0≤  T B    UV 8 ]$;-    ∈ ≥ +   5   UV ⇔  ( ) ( ) ( ) ( ) ( ) ( ) 0 4 2 4 5 43 1 54 1 ≤ − − − − − − − − M M MM M MM M         ⇔ ( ) 0 4 1 4 5 43 1 4 1 ≤ − − − − − −   MM   ⇔ 0229 2 ≤−−   ⇔  11≤≤   #_#;'G,759 =E- { } {AyA|AuAnAmA=  4 798759   ( )    −≤++++ 742 321 (((  ( ) 1≥     UV 8 !,'<- ( )     ++++=+ ((( 2210 1     UV %7_E'7,0@'G,UV,'-  ( ) 1211 1 21 − − ++++=+     (((     UV .JTO,'-      ++++= − (((( 3211 322  P<-UV ⇔ ( )   −≤ − 72 } (   ⇔ ( )   −≤ − 72 1   ⇔ 72 1 ≤+ −     UV "E  +=  V~U '< =VU~• ≥∀>+= − 0122 1     ~UV=EE 1≥∀   %'<-~UYVOu  ;'G,759 UV=E- 3≤  #_#;'G,759 b'=E- { } YAA 1 =         .AAB  CD,0EF'9'G,H2'A'I,'J''''8,$- .'-CK'L2''58,$-  ( ) M M B     − = N  OMN ( ) MM M      − =  –    –!!–!"!"#$%&' 4 7.29R  1 1 + ++ + =          + ∈  A  !,'<- ( ) ( ) ( ) ( )               + + + = + = −+ ++ = + MM M MM M 11 11 1   ' 4 7.AA ∈ 10E  ≤ N  ≤ (.29R-           − − =  8 !,'<-  ( ) ( ) ( ) ( ) ( ) ( ) MM M ( MM M MM M ( MM M              −− = −− − − = − −   O      ( U'V 4 7%. + ∈  (.29R-  1 22 1 22 2 1 + + − −+            UV 8 .',-!3'L2'- 1 1 1 + + + =+        ,'<-         12 1 22 + − =+  P<-UV ⇔ ( ) ( ) ( ) ( ) ( ) ( ) MM M MM M ( 112 2212 1 12 2 1 122212 ++ ++ = + + == +++              O ( ) ( ) ( ) 1 22 2 1 112 22 + + = ++ +      MM M   ' .'-P,9Q0@9(!,'<-  BO ( ) ( ) ( ) ( ) MM M MM M 11 22 1 22 +− +=+ −            O ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) MM MM MM MM 11 2221222 2 1 11 1212 2 ++ ++++ = ++ +++       O ( ) ( )( ) ( ) ( ) ( ) ( ) ( ) 1 22 2 1 11 22 2 1 11 22122 2 1 + + = ++ + = ++ ++        MM M MM M U'V 4 7&. 2≥ 0E + ∈  (.29R-   += + 22 1   UV 8  UV ⇔ 122 1   += +  !,'<- ( ) ( ) ( ) ( ) MM MM M M MM M 12 21 122 12 − +− = − + − =+           O ( ) ( ) ( ) ( ) 2 1 12 1 12 1 + = − + = + +       M M MM M U'V 4 7'.29R –    –!!–!"!"#$%&'  ( ) 2 1 32 112 3 1 2 1 + =++++++ −−                          ((((((  8 !,'<-   = 1   ( ) ( ) ( ) ( ) 1 1 22 2 1 22 22 1 2 −= − − = − − =              M M ( MM M ( M M MM M ((   ( ) ( ) 2 22 33 33 2 3 −= − − =          MM M MM M ((   €€€€€€€€€((  1 1 +−= −         (   €€€€€€€€€(  1 1 = −      (  .&H2'9>0@30@,'-  112 3 1 2 1 32 =− ++++++                         ((((((((((   O ( ) ( ) ( ) 12121 ++++−++−+−+ ((((((    O ( ) 2 1 321 + =++++   (((  U!3'L2'6'7'&V 4 7(.29R  2 1 1 2 1 2 3 4 2 2 3 1 1 2 0 =++++++ + + + +++++                         ((((((  8 !,'<-  ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) MMM MMM MM M - MM M             −++ ++ = ++ ++ − = + ++ 2 11 11 2 1 2   O ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )       +−− + − ++− + = −++ ++ MM MM MM MM MM MM 21 1 1 1 2 1 2 11         O         12 1 1212 2 1 + −− + − + − (   UhV %=,_TO{AAAYA€A0EUhV,'- [...]... 2002 1 2004 + 2002( 2001 2 2004 ' - S = 2004.42003 & ! & F' ; 'G , ( - @ ; 2 3 ' 4 !6 CD 0E , 4 7 A+ -, ( ! ? - (a + b) = $ n Z o'G T0E _ , 8 @ Q6 ( !p < $ 9, _ ; 2004 2004 , 0 @- 2003 J TOY , 47 −4 +2 2 '- !6 5 18 )17 = 18 #_S O |( E 0 18 , 0 18 −2 = B+ @ 7 - S O 18 18 +2 0 U V !pU V 0E U V , ' . O=E9*'  4 78! A ∈ v ^ @ - 355 1 11 1 1 -- -- = − ++ + +         8 !,'< - ( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 1 1 1 1. V.'Z'8 -  ^  - .J ,9Q*2'134  ^  - %7_6',0@0Z'#6'  ^ Y - 66',0@