2l dm m

K = 2 d m = 2lk d 2l dm 2 3 5

3927 1250 = 3.1416 1 10

1 1 2 2 m 1 1 4 4 1 2

m P A P = C 2 5 } 2 = 5 C 14 8

1 36

5 6 7 1 P( 6) + P( 7) + P( 8) = + + = 36 36 36 2 1 36

154 154 250 6 2 250 6 312. 154 1-4 P = G I

SG = S1 1 1 S= 1 4 4 S 1 G P = = 4 = 1 S 1 4 I 1 + m 4 4m 4( 1 ) = + m + m

P = 2 2r = = 1 2 4r 4

1 3 SG P = S I 2 2 1 ( ) = 3 2 1 5 = 9

P 2 1 365 P 3 = 1 365 P4 1 365 P5 1 365 365 P = 1 2 365

1 2 20 365 1 4 1 365 = 1 10 10 1.77 8 P 10 = 1 10 8 10 10 = 0.56 1.77

1 10

m m + m + m 1 m + 1 m m + 1 m m + m + m m 1 m P = m + m + + 1 m + m + 1 m = m + m m +

m m +

[ 1] P = 1 2 [ 2] P = 1 3 1 [ 3] P 4

a 2 1 1 P P 3 2

1 3-3 2 m m + m m m m r ( ) ( ) ( ) = ( ) m + m + m + m +

m P1- r m + m 0.8 = 1-10 1000 m 10 = 0.2 1000 m 1 lg 1000 10 lg0.2

364 365 363 365 362 365 364 365 363 365 362 365 316 365 Λ

8 7 6 5 4 P( ) = 16 15 14 13 12 = 00128. 8 7 6 5 8 P( ) = ( ) 5 = 01282. 16 15 14 13 12 8 7 6 8 7 P( ) = ( ) 10 = 0. 3589 12 15 14 13 12

2 2 R x + y R d d d

1 2 1 3 P = 5 6 = = 01875 2 16.

1 2 P ( k) = C 1 2 k 6 3 1 20 P ( 3) = C66 = = 0. 3125 2 64

1 1-1 k 1 1 k P ( k) = C( )( 1 )

P( k) P( k + 1) P( k) P( k 1) + 1 k = 10 + 1 k = 4 = 2 r = 1 = 1 t k + 1 [ ]

2 2 1 3 0 1 1 1 0 1 1 1 0

a11 a12 Λ a1 a 21 a 22 Λ a2 Λ Λ Λ a m1 a m2 Λ am

2 BAB AB 4 2 3 P 3 1% 1 = = 2. 510 4 2

P P P 1.610 1.26710 4 9-3 -12 1 2 10 = 11 510

x2 = x1 cos60 y1 si60 y2 + x1 si60 y1 cos60 1 x2 = ( x1 3y1) 2 3x1 = 2y2 y1 1 y x y y1 x1 x2 2 3 3 2 1 + = 1 ( ) 2 2 2 2 b c S ABC 3 / 8 a b c 3/ 2 p( p a)( p b)( p c) S 3 p( p a)( p b)( p c) + 3(a + b + c ) / 4 AFCDBE p a b c / 2 S ABC = 1 S 2 AFCDBE 2 2 2

EAC CAG = 1 EAG = 1 120 60 2 2

x = x = 1 1 2 x 1 + x2 x 3 = x x 1x 4x 3 x 2 x1x2x3 - x [ 1 x 1 + x 2 ] - x1x 2[1/ 2 x1 x 2 ] 2 2 1 1 x1 = xy 1 = z1 = ( y + z) y 2 = y1z2 = x2 = ( z1 + x1) 2 2 1 z3 = z2x 3 = y3 = ( x2 + y2 ) Λ 2 limx limy limz h / 3 3 3 xyzlim x y z = h / 3xyz h / 3 x y z y = y z = x = 1 2 1 2 2 x 1 + z1 2 2

k 1 1 C k = 0 2 ( 1) k = 0 k C k 1 1 x = C x k= 0 k x 1 C = ( 1+ 1) = 2 k = 0 k k ( k 1) k = ( 1 C 1) = 0 k= 0 f x f x a C x m k= 0 k k k a1 k=0

1 7 1 7 0 k k k C = 2 2 1 2 16 x y

p c + q dp c q d p q c d 1 2 + 32 + 2 + 3 2 2 + 3 2 2 + 32-2 + 3 2-2 3 1 = 2 + 32 3 = 1 2 + 32 + 2 + 3Λ Λ 2 + 2+ Λ + 2 + 3 1 4 4 44 2 4 4 4 43 2 2+ Λ + 2 + 3 1 4 4 44 2 4 4 4 43 = 1 3 1 2 6 3 + 2 2 = 3 1 2 6 ( 1 + 2 ) = 3 ( 1 2 )( 1 + 2) = 3 1 = 1 2 log ( 3-2 ) ( 3 + 2) 2 3 23 + 2 log 1 a = 1, ( a 0, a 1) log ( a a ( a + 1 + a) = 1 ( a 0) + 1 ) 99 1 3 k = 1 k + k + 1 k + 1 + k k + 1 k 1 99 = ( k + 1 k) = 9 k=1

1 = ( a a1 ) / d k= 1 a + a k k + 1 3x 7 7x+ 3 4 ( 3 2 ) = ( 3 + 2) 3 + 2 3 2 1 3x 7 7( x+ 3) ( 3 2 ) = ( 3 2 ) 5 ( 2 + 3) + ( 2 3) = 4 x 2 32-3 y( 2 + 3) x x ( 2 3) = ( 2 + 3) = y 1 y 2t 3 x 2 x -1 2 6 a b 3-7 a 1 7 a 3-7 3 7 2 1 / 3-7 = 3 7/ 2 2 7 3 0 7-1 / 2 1 1 / 3-7 = 2 7-1 / 2 a 2 * b 7-1 / 2 a2 1 7 ab 4 6 10 1 ( 26 + 5) 1981 198 26 + 5 26-5 0 26 5 = 1 / ( 26 + 5) 1 / ( 5 + 5) = 1 / 10 1981 1981 ( 26 5) ( 1 / 10) (*) 1981 1981 ( 26 + 5) = a + b 26 1981 ( 26 + 5) = a b 26 a b 1981 1981 1981 1981 ( 26 + 5) ( 26 5) ( 26 + 5) ( 26 5) x

1981 * ( 26 5) 1981 0 ( 26 2 a = + 1 + b = 4 + 2 a b x 4 + 2 ( + + 1) 1 ( ( + 1) 2 2 + 1, 4 + 1 a 4 + 2 = b ) 4 + 2 ( + + 1) = 2 + 1 2 ( + 1) /[ 4 + 2 + + + 1] = 1/ [ 4 + 2 + + + 1] { 1/ [ 2 + 1+ 2 ( + 1)]} 1/ [( 2 + + )( 2 + 2)] = 1 / 16 1 ( 1) 1 2 1-2 = -1 1 2 1-2 -1 x + y 2 = (1+ 2) x y = ( 1+ 2) 2 2 x y = [( 1+ 2)( 1 2)] = ( 1) y = [( 1 + 2 ) ( 1 2 ) ] / 2 2, ( = 1, 2, 3, Λ Λ ) 4 4 x y z t ( x y 5) ( z t 5) 4 2 5 a b c a b c a b c p q c a - c p q c a b p q c c 4 4 ( x y 5) + ( z t 5) = 2 5 ( a ± b c ) = p ± q c

3 a9 a a a 4 a a 4 5 a a 5 0 8 a a 8 abc abcabc 7 11 13 abc abc w - xyz 7 11 13 abcw - xyz 7 abc wxyz 7 xyzxyz 7 abc wxyz - xyzxyz abc wxyz - xyzxyz abc w - xyz 1000 71abc w - xyz

2 F 1 2 2 2 2 2 4 2 2 4 2 2 2 2 = 2 = 2 = ( 2 ) = 16 2-2

a a1 a2 a 1 a b c d 2 a b c d / 3 b a c d / 3 c a b d / 3 d a b c / 3 a 11 b 10 c = 9 d = 6 a b c d a b c d a b c d a b c d - 2a b a b d - 2b c a b d - 2c d a b c - 2d 4 a b h 5 a b c d / 3 b a a 7 b 5 c 9 d 5 e 3 f 8 g 5 h 9 a b e d - 2g b a c f - 2h

3 a = 2 17 1 6 6

( - 2)( - 3)( - 4)( - 5) a = a + (1-2)(1-3)(1-4)(1-5) ( 1)( 2)( 4)( 5) b + ( 2 1)( 2 3)( 2 4)( 2 5) ( 1)( 2)( 4)( 5) c + ( 3 1)( 3 2)( 3 4)( 3 5) ( 1)( 2)( 3)( 5) d + ( 4 1)( 4 2)( 4 3)( 4 5) ( 1)( 2)( 3)( 4) e ( 5 1)( 5 2)( 5 3)( 5 4)