General Expansion of Binomials
General Expansion of Binomials
kkk
n xxC 1in oft coefficien theis
General Expansion of Binomials
kkk
n xxC 1in oft coefficien theis
kn
Ckn
General Expansion of Binomials
kkk
n xxC 1in oft coefficien theis
nn
nnnnn xCxCxCCx 22101
kn
Ckn
General Expansion of Binomials
kkk
n xxC 1in oft coefficien theis
nn
nnnnn xCxCxCCx 22101
which extends to; n
nnn
nnnnnnnnn bCabCbaCbaCaCba
1
122
21
10
kn
Ckn
General Expansion of Binomials
kkk
n xxC 1in oft coefficien theis
nn
nnnnn xCxCxCCx 22101
432.. xge
which extends to; n
nnn
nnnnnnnnn bCabCbaCbaCaCba
1
122
21
10
kn
Ckn
General Expansion of Binomials
kkk
n xxC 1in oft coefficien theis
nn
nnnnn xCxCxCCx 22101
432.. xge
which extends to; n
nnn
nnnnnnnnn bCabCbaCbaCaCba
1
122
21
10
4443
3422
243
144
04 33232322 xCxCxCxCC
kn
Ckn
General Expansion of Binomials
kkk
n xxC 1in oft coefficien theis
nn
nnnnn xCxCxCCx 22101
432.. xge
which extends to; n
nnn
nnnnnnnnn bCabCbaCbaCaCba
1
122
21
10
4443
3422
243
144
04 33232322 xCxCxCxCC
432 812162169616 xxxx
kn
Ckn
Pascal’s Triangle Relationships
Pascal’s Triangle Relationships
11 where 1 11
1
nkCCC kn
kn
kn
Pascal’s Triangle Relationships
11 where 1 11
1
nkCCC kn
kn
kn
1111 nn xxx
Pascal’s Triangle Relationships
11 where 1 11
1
nkCCC kn
kn
kn
1111 nn xxx 1
1111
11
11
011
n
nnk
knk
knnn xCxCxCxCCx
Pascal’s Triangle Relationships
11 where 1 11
1
nkCCC kn
kn
kn
1111 nn xxx 1
1111
11
11
011
n
nnk
knk
knnn xCxCxCxCCx
kx of tscoefficienat looking
Pascal’s Triangle Relationships
11 where 1 11
1
nkCCC kn
kn
kn
1111 nn xxx 1
1111
11
11
011
n
nnk
knk
knnn xCxCxCxCCx
kx of tscoefficienat looking
knCLHS
Pascal’s Triangle Relationships
11 where 1 11
1
nkCCC kn
kn
kn
1111 nn xxx 1
1111
11
11
011
n
nnk
knk
knnn xCxCxCxCCx
kx of tscoefficienat looking
knCLHS
Pascal’s Triangle Relationships
11 where 1 11
1
nkCCC kn
kn
kn
1111 nn xxx 1
1111
11
11
011
n
nnk
knk
knnn xCxCxCxCCx
kx of tscoefficienat looking
knCLHS k
nk
n CCRHS 11
1 11
Pascal’s Triangle Relationships
11 where 1 11
1
nkCCC kn
kn
kn
1111 nn xxx 1
1111
11
11
011
n
nnk
knk
knnn xCxCxCxCCx
kx of tscoefficienat looking
knCLHS k
nk
n CCRHS 11
1 11
kn
kn CC 1
11
Pascal’s Triangle Relationships
11 where 1 11
1
nkCCC kn
kn
kn
1111 nn xxx 1
1111
11
11
011
n
nnk
knk
knnn xCxCxCxCCx
kx of tscoefficienat looking
knCLHS k
nk
n CCRHS 11
1 11
kn
kn CC 1
11
k
nk
nk
n CCC 11
1
Pascal’s Triangle Relationships
11 where 1 11
1
nkCCC kn
kn
kn
1111 nn xxx 1
1111
11
11
011
n
nnk
knk
knnn xCxCxCxCCx
kx of tscoefficienat looking
knCLHS k
nk
n CCRHS 11
1 11
kn
kn CC 1
11
k
nk
nk
n CCC 11
1
l"symmetrica is trianglesPascal'"
11 where 2 nkCC knn
kn
Pascal’s Triangle Relationships
11 where 1 11
1
nkCCC kn
kn
kn
1111 nn xxx 1
1111
11
11
011
n
nnk
knk
knnn xCxCxCxCCx
kx of tscoefficienat looking
knCLHS k
nk
n CCRHS 11
1 11
kn
kn CC 1
11
k
nk
nk
n CCC 11
1
l"symmetrica is trianglesPascal'"
11 where 2 nkCC knn
kn
1 3 0 nnn CC
Pascal’s Triangle Relationships
11 where 1 11
1
nkCCC kn
kn
kn
1111 nn xxx 1
1111
11
11
011
n
nnk
knk
knnn xCxCxCxCCx
kx of tscoefficienat looking
knCLHS k
nk
n CCRHS 11
1 11
kn
kn CC 1
11
k
nk
nk
n CCC 11
1
l"symmetrica is trianglesPascal'"
11 where 2 nkCC knn
kn
1 3 0 nnn CC
Exercise 5B; 2ace, 5, 6ac,10ac, 11, 14
