S = 1 2 ( a + b) h a b = a 1 a b = a 1 b b 2 2 πr 2r π π 2 = ( - 2)r 2 2 = - 2 = 57 2r 2r 2

6 5 7 4 3 6 5 4 3 3 4 5 6 7 7 5 7 6

1 1 1 1 1 2 3 5 7 7. 2 3 4 6 12 3 4 12 12 1 1 1 1 5 1 7 2 3 12 6 4 3 12 2 12 3 4

3 7 = 21 8 + 4 =12 + + + = 18 + - + = 4 + + - = 8

1 2 1 2 1 2 1 2 1 2 1 2 1 4 8 4 2 1?

222222222 4 1 1 2 2 2 1 333333333 4.5 2 3 1 4444444444.5 2 4 555555555 9 5 1 1 666666666 9 2 3 777777777 4 1 1 1 2 2 7 1 1 888888888 10 1.25 3 3 2 1 999999999 9 3 6

222 14 2 43 2 555 1 4 2 43 5 = 123456789876543210 2 5

1 1997 + 2 1997 + 3 1997 + + 1997 1997 = 1 2 3 1997 + + + Λ + 1997 1997 1997 1997 ( 1+ 1997) 1997 2 = 1997 = ( 1+ 1997) 2 = 999

1 31 + 2 31 + 3 31 + + 30 31 = 1 2 3 30 1 + 30 30 2 31 15 + + + + = ( ) ( ) = = 15 31 31 31 31 31 31 1 31 + 2 31 + 3 31 + Λ + 30 = 1 30 2 = 15 31

1-9 10 9 9 100 9 1000 10000 =? 1-9 9 9 9 10 100 1000 10000 = 1 - ( 0.9 + 0.09 + 0.009 + 0.0009) = 1-0.9999 = 0.0001

1 3 24 + 2 6 48 + 3 9 72 =? 1 2 4 + 2 4 8 + 3 6 12 1 3 24 + 2 6 48 + 3 9 72 1 2 4 + 2 4 8 + 3 6 12 3 24 1+ 8 + 27 = 1 ( ) 1 2 4 ( 1+ 8 + 27) = 9

41 3939 = 4141 41 3939 4141 39 (100 +1) = 41 41 (100 +1) = 39

1 1 1 1 = = 2 3 6 2 3 1 1 1 1 = = 3 4 12 3 4 1 1 1 1 = = 4 5 20 4 5 1 1 1 1 1 1 1 + + + + + + =? 2 6 12 20 30 42 56 1 1 1 1 1 1 1 + + + + + + 2 6 12 20 30 42 56 1 1 1 1 1 1 1 = + + + + + + 1 2 2 3 3 4 4 5 5 6 6 7 7 8 1 1 1 1 1 1 1 1 1 1 1 1 1 = 1 + + + + + + 2 2 3 3 4 4 5 5 6 6 7 7 8 = 1 1 8 = 7 8

1 1 =? 2 1 1 1 =? 2 4 1 1 1 1 =? 2 4 8 1 1 1 1 1 =? 2 4 8 64 1 1 1 1 1 =? 2 4 8 256 1 1 1 1 1 1 = 2 4 8 64 64 1 1 1 1 1 1 = 2 4 8 256 256 1 2 + 1 4 + 1 8 + + 1 2 n

1997 1994 1995 1996 1998 1995 1996 1997 1997 1 1994 1 1 1 1998 1998 1995 1995 1995 1 1996 1 1 1 1996 1996 1997 1997 1 1 1 1 1998 1995 1996 1997 1 1 1 1 > > > 1995 1996 1997 1998 1994 1995 1996 1997 < < < 1995 1996 1997 1998

1 1 1 1 A = 1 + + 10 100 1000 10000 1 1 1 1 B = 1 10 100 1000 10000 1 1 1 1 C = 1 + + 10 100 1000 10000 1 1 1 1 D = 1 + 10 100 1000 10000 E = 1 10 100 1000 10000 0

1 = 1 2 3 4 1 1 1 Λ 1996 1998 1997 5 1997 1996 5 1 1 Λ 3 1 4 2 = 1998

777 1 4 2 43 7 999 1 4 2 43 9 = 8 7 8 9 777 1 4 2 43 7 999 1 4 2 43 9 = 7777777622222223 8 7 8 9 777 1 4 2 43 7 999 1 4 2 43 9 m 7 m 9 777 1 4 2 43 76222 1 44 2 4 43 23 (m-1) 7 (m-1) 2

333 1 4 2 43 3 2 = 3 2 333 1 4 2 43 3 = 111111110888888889 3 2 333 1 4 2 43 3 = 111 1 4 2 4 3 10888 1 4 2 4 3 89 n 3 (n-1) 1 ( n 1) 8

999 1 4 2 43 9 999 1 4 2 43 9 88 88 999 1 4 2 43 9 999 1 4 2 43 9 m 1 0 m m

2750 1875 1875 = 22 5 250 125 125 = 22 5 26 15 15 = 22 5 22 5 5

5 5 7 7 + + 9 11 8 15 1 1 3 3 + + 5 8 4 8 5 5 ( 9 + 11) 5 100 + = = = 1 1 9 11 9 11 99 99 7 7 ( 8 + 15) 7 161 + = = = 1 41 8 15 8 15 120 120 1 1 5 8 13 + = + 5 8 5 8 = 40 3 3 ( 4 + 8) 3 36 + = = = 1 1 4 8 4 8 32 8

1 2 + 3 3 1 2 3 4 + + + 5 5 5 5 1 2 3 6 + + + Λ + 7 7 7 7 1 2 3 7 + + + Λ + 8 8 8 8 1 1 3 19 + + + Λ + 20 10 20 20 1 2 + = ( 3 1) 2 = 1 3 3 1 2 4 + + Λ + = ( 5 1) 2 = 2 5 5 5 1 2 3 6 + + + Λ + = ( 7 1) 2 = 3 7 7 7 7 2-1 2 1 8 1 3 + + + Λ + 4 8 1 2 = 8 2 = 4 1 2 7 8 = 3 1 2 1 1 3 19 + + + Λ + 20 10 20 20 1 = 20 2 2 = 10 1 2 = 9 1 2

1 1 2 1 1 1 3 3 1 1 1 4 4 1 1 5 5 6 9 10 1 1 6 + 1 1 12 + 1 20 + 30 + 42 1 1 1 1 = = 2 3 2 3 6 1 1 1 1 = = 3 4 3 4 12 1 1 1 1 = = 4 5 4 5 20 1 1 1 1 = = 5 6 5 6 30 1 1 1 1 = = 9 10 9 10 90 1 1 1 1 1 + + + + 6 12 20 30 42 1 1 1 1 1 = + + + + 2 3 3 4 4 5 5 6 6 7 1 1 1 1 1 1 1 1 1 1 = + + + + 2 3 3 4 4 5 5 6 6 7 1 1 1 1 1 1 1 1 1 1 = + + + + 2 3 3 4 4 5 5 6 6 7 1 1 = 2 7 7 = 2 2 7 5 = 14

= 29.5 29

= 259.5 259

= 244.5 244 = 244.5 244

3 = 56 100 4 3 152 375 = 152 1000 = 57000 8 7 48 875 = 48 1000 = 42000 8

1 9 0.111 0.1& 2 9 0.222 0.2& 0.1& 2 3 9 0.333 0.3& 0.1& 3 4 9 = 0. 444 = 0. 4 & = 0.1& 4 8 9 = 0. 888 = 0. 8 & = 0.1& 8 13 9 = 9 +4 9 = 1.4& 35 9 27 8 9 3.8& 16 36 = 16 4 36 4 = 4 9 = 0.4& 88 72 = 88 8 72 8 = 11 9 = 1.2& 640 720 8 9 0.8& 17 0.9 = 170 9 = 17 9 10 = 1.88 10 = 18.8&

1 99 0.010101 && 2 99 0.020202 && 0.01 && 2 3 99 0.030303 && 0.01 && 3 4 99 = 0. 040404 = 0. 04 && = 0. 01 && 4 9 99 0.090909 && 0.01 && 9 17 99 = 0.01& 17 = 0.17 && 92 99 0.01& 92 0.92 && 123 99 99 24 99 1.24 && 80 99 0.01 && 80 0.80 && 500 99 = 5 99 100 0.05 && 100 5.05 && 6 9.9 60 99 6 99 10 = 0.06 && 10 0.60 && 6.3 99 = 63 99 10 = 0.063 && 5.24 0.99 524 495 29 = 5 0.29 && = 5.29 &&

1 11 0.090909 && 2 11 0.181818 && 0. 09 && 2 3 11 0.272727 && = 0.09 && 3 4 11 0.363636 && 0.09 && 4 9 11 0.818181 && 0.09 && 9 10 11 0.909090 0.9& 0.09 && 10 30 11 = 3 11 10 = 2.72 && 18 11 = 11 7 11= 1.63 && 57 11 55 2 11 5.18 && 67 22 11 2 6.09 && 2 3.045 && 81 55 11 5 81 11 5 = 7.36 && 5 = 1.472 && 2.4 11 = 24 11 10 = 2.18 && 10 = 0.218 && 91 77 13 11 1.18 && 2001 11 2000 1 11 181.818 && + 0.09 && = 181.90 && 100 88 = 100 11 8 = 9.09 && 8 = 1.136 &&

1 111 0.009009009 & & 2 111 0.018018018 & & 0.009 & & 2 3 111 0.027027027 & & 0.009 & & 3 4 111= 0.036036036 & & 0.009 & & 4 9 111 0.081081081 & & 0.009 & & 9 10 111 0.090090090 0.090 & & 0.009 & & 10 11 111 0.099099099 & & 0.009 & & 11 17 111 0.009 & & 17 0.153 & & 25 111 0.009 & & 25 0.225 & & 37 111 0.009 & & 37 0.3& 72 111= 0.009 & & 72 = 0.648 & & 138 111 = 111+ 27 111 = 1.243 & &

22 1 3 1 8 1 4 1 3 1 1 8 1 4 22 1 1 4 1 8 22 13 8 22 8 11 = 16 16 1 8 = 2 16 1 4 = 4

x + 3 x = 3 2 2x = 6 x 3 x 9

1 5 4 5 1 4 1 x 5 x = x 5 1 x 4 x = x 4 1 - x 5 = 1- x 4 4 1 - x 5 = 4 - x x - x 5 = 4-1 4 5 x = 3 x = 33 / 4 3 3 4

1 11 13 3 11 11 13 = 24 1 1 24 = 11 3 36 13 1 1 24 = 13 3 36 13 8 36-11 36 1 = 8 18 = 144 1 144 3 = 48 11 144 36 = 44 13 144 36 = 52

44 52 1-1 1 3 3 2 1 = 96 3 3 3 1 = 96 2 3 = 48

1 1 3 2 3 2 1 1 7 1 + 6 2 3 1 7 6 1 1+ 6 2-1 3 1 = 7 6 = 42 1 42 2-6 = 15 1 42 1 = 15 3

1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 1 1 1 = 2 2 2 2 = 16

1 4 1 4 4 = 1 3 2 + 1 2 4 1 = 6 + 2 1 = 6 2

1 3 1 3 1 3 3

1 5 1 5 1 1 1 5 5 5

1 2 18-2 3 + 1 1- = 16 4 = 6 3 3

1 1 6 3 1 6 + 1 3 + 1 2 = 1 6 + 2 6 + 3 6 = 1

1 2 1 2

1 1 1 1 2 2 2 2 3 5 3 5 4 6 4 7 5 9 9 9 6 10 10 11 7 13 11 13 8 14 12 15

10 9 10 10 10 20 19 8 10 18 10 9 8 7 6 5 4 3 2 1 1 = 20 19 18 17 16 15 14 13 12 11 184756 95 55 = 100 184756 90 60 = 2025 184756 85 65 = 14400 184756 80 70 = 44100 184756 75 = 63504 184756

1 1 54 53 1 1 1 = 54 53 2862

2 2 2 a a a 2 2 2 a π a a 2 = π 4 = π 4 π 2 2 2 π 2 2 a a a a a 1 π 4 4 = 2 = 2 4 a a π = 1 1 0785. = 215%. 4

8 8 2 2 = 32 2 2 2 2 πr 2r π 2 r π 2 114 2 = ( ) 2 =. = = 57% 2r 2r 2 2

a 3 2 a a = 2 4 3 3 a a π 3 3 3 a a a 1 4 = π 4 = π 4 3 a π 1 4 π 3 = 1 = 1 0. 785 = 215%. a 4

3 r 2-4 3 4r = 2-4 4 = 2.28 4 = 0.57 = 57

1 2 2 6 = 8 3

1 4-1 2 4 4 4 2 = 4-8 = 12.56-8 = 4.56

1 2-1 2 2 2 2 4 2 = - 2 2 = 2-4 = 2.28

1 2 2 8 2-8 2 2 2 = 8-4 = 4 = 12.56

1 8 4 1 2 1 2 8 2 2 3.143.14 8 2 2 2 = 3.14 4 3.14 8 = 1 4 1 4 1 1 4 2 = 1 8 1-1 = 1 4 8 8 2 1 3.14 8 8 = 25.12

1 1 2 2 1 4 1 1 3.14 7 2-5 2 2 4 = 9.42

90 20 20 2 3.14 20 2 360 2 = 314-200 2 = 114 2 = 228 2 90 3.14 20 2-20 20 360 = 3.14 2-400 = 228

8 2 1 3.14 2 2-8 8 8 2 + 8 2 2-3.14 8 2 1 2 2 = 25.12-16 + 32-25.12 = 16 8 8 2 2 2 2 = 16 2 2 = 16

5 ABD 8 5 12 8 = 19.2

1 2 + 2 2 4-2 + 2 2 3-2 2 2 1 = 4 8-4 2 3-4 2 = 32-12 - 4 = 16

6 2 314. 2 60 3 = 9.42 360