*- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5...
Transcript of *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5...
![Page 1: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/1.jpg)
sNx(cxxr.
c1EXYc:XmY”
5::CG5
G! _.
Xl I--.
-.,cti
5>:*-_IT=._
![Page 2: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/2.jpg)
c+YxxilJii~4 Tmmhln~ -n !(n-l)!
i&j, - =(nf I)!
n.(n-l).(n-2). . . . 3.2.1(n-l).(n-2). . . . 3.2.1
n
~l~t3!Jfll3(2)LW3lZh n! = nx(n-I)!
61 n = 19::$&il
I! = 1X(1-1)!
1 = 1x0!
1 =O!t ‘3uwm O! = 1
fjjfil - =(n+2)! (n+2).(n+I).n.(n-1). . . . .4.3.2.1,n ! n.(n-l).(n-2). . . . .4.3.2.1
= (n+2).(n+l)
= n2+3n+2
4. 9!
7 . n!x(n+2)!(n+3)!
n!x(n-3)!lo’ (n-l)!x(n-4)!
8, (n-3)!x(n-6)!(n - l)!
(3)
154 MA 103
![Page 3: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/3.jpg)
\ aIn 4 \ Qlr.l4
MA 103 155
![Page 4: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/4.jpg)
156 MA 103
![Page 5: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/5.jpg)
MA 103
GGG, GGP, GGF, GPG, GPP, GPF, GFG, GFP, GFF, PGG, PGP,
PGF, PPG, PPP, PPF, PFG, PFP, PFF, FGG, FGP, FGF, FPG, FPP,
FPF. FFG, FFP, FFF.
157
![Page 6: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/6.jpg)
158 h4A 103
![Page 7: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/7.jpg)
MA 103 159
![Page 8: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/8.jpg)
M A 103
![Page 9: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/9.jpg)
MA 103
![Page 10: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/10.jpg)
4!4p4 = -(4-4)!
4!zz-O!
4!=-1
= 4x3~2~1
= 24
162 MA 103
![Page 11: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/11.jpg)
5!“p, = 5P3 = (5 -3)!
5!ZZ-2!
= 5x4~3~2~12x1
“P, = 4F’z = $&jj
4!=-2!
= 4x3~2~12x1
wflnasbQuufex:96
1224, 1242, 1422, 2214, 2241, 2142, 2412, 2124, 2421, 4122, 4212, 4221,
ez:%Canv4 ga 12 Bipaau
MA 103 163
![Page 12: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/12.jpg)
3!=z
= 3 Biuau to
122, 212 mr 221
9!= 4!
= 3780 %
164 MA 103
![Page 13: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/13.jpg)
MA 103 165
![Page 14: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/14.jpg)
166 MA 103
![Page 15: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/15.jpg)
1“C,., = (n-r)! &n+r)!
1
= (*-Xi r!
n != r! (n-r)!
MA 103 167
![Page 16: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/16.jpg)
15x14x13x12x11x10!=5x4x3x2x1x10!
5X4X3!= 3!x2xl
1
2! ;,;-2,!- = 66
nfn-1) = 1 3 2
n’-n--132 = 0
(n+ll)(n-12) = 0
n = -11, 12Y
tlislxu n = 12
1 6 % MA 103
![Page 17: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/17.jpg)
ii31 ‘c. = 9:_----5! I’
MA 103 169
![Page 18: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/18.jpg)
7!=-3! 4!
= 7x6x5x4!3x2x4!
170 MA 103
![Page 19: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/19.jpg)
MA 103 171
![Page 20: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/20.jpg)
+( .r,) ab”-‘+( i) a’b”
= a”+na”-lb +nl)anmzb2 +...+n(n-l)...(n-r+l)a”-‘b’2! r.I
+...+nab”-‘ib”
= a + b
172
+k(k-l)...(k-r+l)r !
akW + . . . +kabkm’+bk
MA 103
![Page 21: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/21.jpg)
(a+b)“” = ak+‘+kakb+.,.+ k(k-I)...(k-r+I)ak-r+,b’r !
+...+k(k-I)...(k-r+2)at-r+,br + +b~+,(r-l)!
. . . . . . . . . . (1 )
= ak+i+(k+l) akb+. + @+I)k...(k-r+2) alr-r+,br. .r !
+...+b”’ . . . . . . . (2)
k(k-l)...(k-r+2) k-r+l+l(r-l)! [ r I
= k(k-I)...(k-r+2) k - r + l + r(r - I)! [ r I
= (k+I)k(k-l)...(k-r+2)(r - I)!r
= (k+l)k...(k-r+2)r !
MA 103 173
![Page 22: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/22.jpg)
A
J/12/ \,\,-0,14/ \ 1\,/ \
,,~~~“~~5X)~,,
174MA 103
![Page 23: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/23.jpg)
(“:‘) = (,“J+(:>n !Gtlyd (,!I,>+(:> = ~jrr+l,!+&gm! (n-r+l)n!z
r(r-l)! (n-r+l)! + r!(n-r+ 1) (n-r)!
m! +(n-r+l) n!= r!(n-r+l)! r!(n-r+l)!
m! +(n-r+ l)n!zr!(n-r+l)!
= jr+(n-r+l)Jn!r!(n-r+l)!
(n+l)n!= r!(n-r+l)!
(n+l)!= r!(n-r+l)!
= (y’)
MA 103
#
175
![Page 24: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/24.jpg)
3%?!1 (a-tb)’ = a5+5a4b+----‘X4 a’52 5x41x2 T __ a%’ -t Sab’ + bS
1x2
24 = (lil)'
176
![Page 25: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/25.jpg)
= 673,5Y6xe #
= &KiiXiOX9Xr3!41x8! P*qJ
= 495 p8q4 #
177M A 1 0 3
![Page 26: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/26.jpg)
12x11x10x9x8x7!=5! x7! aI4 (32b5)
= 792 x 32 a’4b5
= 25344 a14b5
bllfL:a9J-ln II = 12, r = 4
= 7920 a16b”
= 1’+8(1’) (.Ol)+y (16) (.01)2 +8x;x6 (1’) (.01)3
+8x74q6x5 (14) (.01)4+...
= 1+.08+.0028+.000056+.0000007+...
= 1.082856
(1.01)8 = 1 +8(.01)
= 1+.08
= 1.08v,
6.Rk.J (1 .Ol)* %lIhJlIU 1.08
178 Mfi 103
![Page 27: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/27.jpg)
%I 1 wJo7 asI%Ylqwguwn9ulu n%~slerL~oaJdo~d~
1 . (a+b)6
2. (2x + y2y
3 . (x2 - 2y)6
4. (2x + y*))
5 . (x2-3y)4
6. (ia+2b)”
7. (2a2- b)’
ml%l8 drh9 wvl1bmwil9 "T
8. b~OB1d 3 Y89n14n%tP10 (~+2)~
9. rila8J~ 5 "uo9n15n5~oler(x+2y3)"
18. wLLW@14dli~o(~) = (;)+(;)+(;)+(;)+...+(;)
= 2”
19. =JwelS11(~)-(; )+(;)-(;)+.A(;) = 0
MA 103 179
![Page 28: *- I>: T=. - e-book.ram.edue-book.ram.edu/e-book/m/MA103(41)/ma103(41)-6.pdf · “p, = 5P3 = (5 5!-3)! 5! ZZ-2! = 5x4~3~2~1 2x1 “P, = 4F’z = $&jj ... T __ a%’ -t Sab’ + bS](https://reader031.fdocuments.net/reader031/viewer/2022020413/5b8c657409d3f236638ce994/html5/thumbnails/28.jpg)
Yw&Ju
22. (l.co4)’
23. (.993)3
24. (395)”
25. (.989)’
MA 103