1309736416
DESCRIPTION
-TRANSCRIPT
4 (Binomial Theorem)
4 (Binomial Theorem)1(Binomial Theorem
(Binomial Theorem)
1. 2. 3. 4.
(a b) a , b n n 4.1 (Factorial)
n n!
n n n! = n(n-1)(n-2)(n-3)..3.2.1
4.1
1) 4!
2) 7!
3) 10!
1) 4! = 4 3 2 1 = 24
2) 7!= 7 6 5 4 3 2 1= 5,040
3) 10!= 10 9 8 7 6 5 4 3 2 1 = 3,628,800
n! n
n!=n(n-1)!
=n(n-1)(n-2)!
=n(n-1)(n-2)(n-3)!
=n(n-1)(n-2)(n-3)(n-4)!
n!=n(n-1)!
n= 1 ;
1!=1(1-1)!
1=1(0!)
0!=1
4.2 1)
2)
1)
=
= 42
2)
=
=
4.3 1)
2)
1)
=
=
=
=
=
2)
=
=
=
4.4
n = 5
=
=
=
=120
4.5
=30 n
= 30
=30
(n+2)(n+1)=30
(n+2)(n+1)=(6)(5)
;
n=4
4.6 1) 1211 10
2) 27
3) n- 5n + 6
4) (2n+2)(2n+1)(2n)
1) 1211 10
=
=
2) 27
=
=
3) n- 5n + 6
= ( n-2)(n-3)
=
=
4) (2n+2)(2n+1)(2n)=
=
4.11. 1.1 8!= . .. ..1.2 = .. ..1.3 ..1.4 .. .. ..1.5 .. ..2. 2.1 . ... ... .2.2 . ... ... ...2.3 n = 8
. ... ... .2.4 n = 7
. ... ... .3. n 3.1
= 930
...... ...3.2 = 132
...... ...3.3
= 16
...... ...4. 4.1 65 64 ..
4.2 13 .
4.3 (n+5)
4.4 (2n-5)(2n-6)(2n-7) ..
4.5 n+ 30 .
4.2 (Binomial Coeficient)
n , r nr
n , r 0 =
4.7 1)
4)
2)
5)
3)
1)
=
=
=
= 20
2)
=
=
=
= 21
3)
=
=
=
=
= 21
4)
=
=
= 1
5)
=
=
=
= 1
=
=
=
4.8
=15 n
= 15
=15
= 15
= 15
n(n-1)(n-2)(n-3)
=15( 4321)
n(n-1)(n-2)(n-3)
=(35)( 4321)
n(n-1)(n-2)(n-3)
=(32)(5)(4)(3)(2)
;
n=6
4.9 +-
+-
= +-
= +-
= +-
=+-
= 126 + 210 10
= 137
4.2
1. 1.1 ..
..
1.2 .
..
1.3 .
..
2. +-
..................
3. = 56 n
..................
4.
EMBED Equation.3 +
EMBED Equation.3 +
EMBED Equation.3 ..................5. ....6. = 2 n
..................7. =
EMBED Equation.3 n
..................
4.3 (Pascals Triangle)
Blaise Pascal
EMBED Equation.3
4.3.1 4.3.2 1
4.3.3 2
4.3.4 n n + 1
4.3.5 n
(1) (2) () () - 0
- 1
- 2
.
- 0
0
0
(3)
(4)
(5) 4.4
4.10
(a) = x (b) = 2y ;
(x+2y)= (x)+(x)(2y)+(x)(2y)+(x)(2y)+x(2y)+(2y)
=
=
=
4.11
=
= 16a
EMBED Equation.3 (9y)
=
=
4.12 4
4.13
24-3r=0
24 = 3r
=r
8=r
8 + 1 9
4.13
4 7
4.15
a = x b = (3x 1) ;
= x
EMBED Equation.3 x(3x-1) + x(9x- 6x + 1)
+ (3x)+3(3x)(-1)+3(3x)(-1)+(-1)
4.16 4
= (3+0.02)
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
+0.00000016
= 0.83.1817
(3.02) = 83.1817
6.3
1.
............2.
.............3. 4
.......4.
5.
..........6.
..............********************** ***************** n r EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3 EMBED Equation.3
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