365 1 4 29 499 940 91 5 16 23 11 16

29 43 81

3 3 4 365 1 4 21 1 4

10 730 = 31466. 10 232

29 773 1457 20 4 365 145 589 1825 7 3.1 47

1825 7 47 27 3303 104 5969 1488 1 0.054 47 A B 1 = 589 589 B 1488 47

a + (b - a)a = 1 2 2 2 2 2 2 [c - (b- a) ] a a = c - (c - a ) a 2 2 2 (c- a) + 2a(c a) = c a c a, c = ( c a) 2 2 2 2 2 2 2 + a c + a = b c - a = b (c+ a) + b (c + a) - b c = a = c -1 c + a 2(c+ a) 2(c + a) b c - b c + b c - b c + b c b a = 2( c a)( c b) + ( c b) b = 2( c a)( c b) + ( c a) c = 2( c a)( c b) + ( c b) + ( c a); 2 2 2 2 1 2c (b a),b a = 2c (b + a), a, b b = 2 1 [a + b) + (b a)], a = [(a + b) (b a)]; 2 2 2 ( c + b) ( c b) = ( 2c) 4a, ( c + a) ( c a) = ( 2c) 4b 2 2 ( )

= 10

63 9 + 7 a1b2 + a2 b1 b + b 1 2 a 1b2 + a2 b1 b 1 + b 2 a1b 2 + a 2b1 b + b 1 2

A B = a b B = Ab a

V = 1 2 (b + b )ah 1 2 1 (b1 + b 2) a h, 4. 2 3 2 A a x + 3a x x = A a 3 3 5 A - a x 2 2 3a x 3a x, x. 1 1 3 1 1 1 1 1 1 S = 1 2 Lr S L r lim ln = 0,lim Ln = L,limSn = S 6 n n n liml = 0 lim r = 0,lim[ S + 2( S + 1 S )] = S n n n n n n n n n S = lim 6 2 1 1 l nrn = Lr n 2 2 1 1 1 1 1

V y = 1 V 3 abh = 1 6 abh a b h b 1 V y:v b = 2:1 2 1 1 4 4

2 l 1 l 2 l 3 l4 S4 = 313 584 625 2 2 2 S5 = 314 64 S4 + 2( S5 S4) = 314 169 S 625 625 S = 314 4 2 = 3927 / 25 1250 l 8 S 9 r N = a + a r 2a + 1

1 6 abh

a am + cn c > > b bm + dn d a c m n b d

26 49 9 17 17 1 9 17 9 17 43 81 26 49 26 49 9 17 26 49 43 81 26 49

13 221 600 27.321604

157 50 ( 3927 = 3.14 = 3.1416 1250

355 22 ( ) ( ) 113 7 = 3 + 1 1 1 1 + + + + = [3 7 15 7 15 1 292

1 22 = 3+ = 7 7 1 1 333 = 3+ + = 7 15 106 1 1 1 355 = 3+ + + = 7 15 1 113 1 1 1 1 = 3+ + + + = 7 15 1 292 103993 33102 = 3.141509431 P Q 103993 ( 33102 33102 355 52163 113 16604 355 16604 113 a c m n b d ma + nc 157 22 mb + nd 50 7 1571 + 229 355 = 501 + 79 113 3 22 3 1+ 2216 355 = 1 7 11 + 716 113 355 113 355 113 355 355 18751950 113 113

355 113 22 7 2 r 2 3 3 = 2 r r 2r 3 2 4 ( ) = ( ) 4

365 1 4 1 77 1 365 9589 14423804 = 14424644 39491 39491 860 860 45 11 = 0.99993 1 45 11 39491 39491 12

V = 3 2 R 3 R 1 6

1 8 1 8 4 3 1 8 1 3 1 3 3 1 3 2 3 R R R R = R 3 3 2 3 2 3 16 3 8 R = R 3 3 16 3 4 3 V= R 4 = R 3 3

27 1255 2263 0.8 1 76.53 1 409 5 46644.

1 2 2 t + t t T = T0 + + ( 1 2) 2 ( 1 2) l 2 l 2l t = 16 10 = 14. 54 11 l = 17 = 1545. 11

t 0 t 0 t 0 = 0.1 15 0 t 0 1 K = K a t L t 0( 0 0 ) 0

M g = 15 96,

( 300 d) 1242 d H = = ( 12 ) 300 103. 5 25

( m 1) n nh + n = 61 h 2 16069 110 = = 25 15409 46644 46644 46644

à

K z 0 0 K0Z0 Kn = K 1 47. 8

g = 3523. 9339 183 B

λ l = 1 l Z l 3300 ( 18 ) l

4 B = 19 ( 639 1 2 119 37 ), 4930801 A E G = 13500, 371986. 97 13500

1 V M = M M 3300 ( 182 ), 1 V M = M M 3435 ( 1818682. ) 1 144 F = 1315 S S S S 10000 [( 1 10 ) 1690 ( 4566 ) ] 193 81305 P = ( m) m, 350000 386 1733 314440 8281 P = ( m) m, 2100000 1733 10500

184 16 2 4 T = W W 50025 50025 3335 Y = 1 1752 + Q 100 1 Y = 2748 - Q 100 460 2 8 Q = W W 4, 6003 4004001

K ( 1480 ) R = 10 + 10, 1480 1480 34 N = ( ), 100 2000 1000 1337 41 1000N = ( 2000 ), 100 1337

A A 1 1 / 1 / C 1 2 / 1 / C C 1 2 3 / 1 / C C C n n-1 n-2 2 n n-1 3 n n 1 n -1 / 1 2 3 4 C n 1 / 1 1 1 1 C 1 2 3 n-1 n m n + 1 1 C C C C C C n n n n 1 C n n n n n n

4 1336336

( a + b) c = 2( c a)( c b) a = 2( c a)( c b) + ( c b) b = 2( c a)( c b) + ( c a) 2ab ( a + b) c = = d a + b + c

1 1 i(i l)(i + 2) ( r + p -1) = r(r +1)(r 2) ( r + p) p = 1 p! (p +1)!

h V = h b d a d b c b [( 2 + ) + ( 2 + ) ] + b ( c a)

2 2b d d 2 2 l = + c c = 2 ( ) ( b) d 2 2

3 1 2 1

( 1) 1, ( 2) 1 2 2 D = a11 b10 D = a10 b11, 2 2 ( 3) 1, ( 4) 1 2 2 D = D13 b1 D = b13 a1, 2 2 2 2 ( 5) r = b2 b15, ( 6) r = a14 a3,

b = a 1 a b 1 11 l1 x2 + 230x + 6000 = 200 x 2 2[ x + 230x + 6000 2x( 200 x)] = 200 x 2 6x 340x + 12000 = 200 x 1 2 D 2 = b a 10 11

3 3 2 2 x yz = 5760,( = [ ] 4 4 2 2 x y + x + = 113, 2 2 z + 34 = y

x = 20 2 3

x = 100x = 100(8 + x ) = 100(8 + x 3 10 ) = 840 1 2

M ki = 1(modA ) i 1 2 3 n A i N R k M R k M 1 1 + 2 2 + R + nk A A 1 n i 2 N = R k M i i pm, A i= 1 i n M A n (mod M), k M i 1(mod A i ) A i G = M i A A G g A G g (moda ), i i i i i i i i

2 2 2 1 a + b c 2 2 2 A = [ a b ( ) ], 4 2 a b c ( A = s( s a)( s b)( s c), s = + + 2

V h 2 2 = ( a + b + ab) 3 n b a S = a + b + ab + 2 2 ( ) 3 2

b a 2 a + (a + 1) + (a + 2) + + (b -1) + b = n 2 2 2 2 2 2 2 b -1 (a + b + ab + 3 2 )(1) n 2 2 2 2 1 + 2 + 3 + + n = (n +1)(n + 1 ), (2) 3 2 n( n + 1) 1+ 3 + 6+ 10+ = n (n +1)(n + 2), (3) 2 6 ab + (a +1)(b +1) + (a + 2)(b + 2) + + ( c 1)( d 1) + cd n = 6 2 + + 2 n [( b d) a ( d + b) c ] + ( c a ) (4) 6 237 56 112 237 = 118.5 112 118.5 2

n( a + a S = 1 n ) 2