sNx(cxxr.

c1EXYc:XmY”

5::CG5

G! _.

Xl I--.

-.,cti

5>:*-_IT=._

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

\ aIn 4 \ Qlr.l4

MA 103 155

156 MA 103

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

158 h4A 103

MA 103 159

M A 103

MA 103

4!4p4 = -(4-4)!

4!zz-O!

4!=-1

= 4x3~2~1

= 24

162 MA 103

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

3!=z

= 3 Biuau to

122, 212 mr 221

9!= 4!

= 3780 %

164 MA 103

MA 103 165

166 MA 103

1“C,., = (n-r)! &n+r)!

1

= (*-Xi r!

n != r! (n-r)!

MA 103 167

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

ii31 ‘c. = 9:_----5! I’

MA 103 169

7!=-3! 4!

= 7x6x5x4!3x2x4!

170 MA 103

MA 103 171

+( .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

(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

A

J/12/ \,\,-0,14/ \ 1\,/ \

,,~~~“~~5X)~,,

174MA 103

(“:‘) = (,“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

3%?!1 (a-tb)’ = a5+5a4b+----‘X4 a’52 5x41x2 T __ a%’ -t Sab’ + bS

1x2

24 = (lil)'

176

= 673,5Y6xe #

= &KiiXiOX9Xr3!41x8! P*qJ

= 495 p8q4 #

177M A 1 0 3

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

%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

Yw&Ju

22. (l.co4)’

23. (.993)3

24. (395)”

25. (.989)’

MA 103