1 4 5 2 3 = = 0.618

2 3 1 3 3

2 3 2 x + 1 2 + 1 +1 = 37 3 7 1554 x 97

= = 100 20 2

5 80 7 1 14 2 7 1 5 21 21-11 10 2 14

1 1 6 5 1 1 1 3 4 3 2 1 1 1 6 5 1-1 1 = 5 1 = 1 1 1 1 6 5 6 5 6 4 3 2 1-2 1 = 4 1 1 1-3 1 3 1 1 1-4 1 2 6 4 6 4 6 6 3 6 3 6 6 2 6 1 = 1 5 1-5 6 6 = 1 1 2 6 6 1 3 3 18 6

= + = 8

6 1 6 2 = 3 2

22 7 355 113 3.14 3.141592 22 7 355 115

1 1 2 1 1 2 1 1 2 = 3 1 3 2 4 4 1 3 2 = 7 4 8 7 3 8

1 1 x X x 6 12 x + x 12 + x 7 + 5+ x 2 + 4 = x 6 9 x = 9 84 x = 84

1 3 1 150 17 1 1 1-1 3 3 1 = 2 1-1 51 3-2 51 = 32 32 150 17 51 51 51 = 150 = 239 1 32 16 1 150 16 1 16

AHHAAH = HA JOKE AHHAAH AHHAAH = HA = JOKE JOKE HA AHHAAH HA AH10000 + HA100 + AH = HA 10001AH = 100 + HA 73 137 100 AH HA

3 7 52 8 10 2 3 4 1 3

1 3 2 10 8 52 3 2 3 7 2 10 8 52 7 2 3 4 3 2 10-8 +52 7 1+ 3 2 4 3 3 2 10 8 52 7 1 3 2 4 3 3 2 10 8 52 7 1 3 2 4 3 4 1 = 64 7 = 128 2 7 3 1 3 3 2 1 3 m 52 8 10 2 m 2 10 8 52 3 2

l l' l 0.618

1 2 2 1 3 3 1 4 4 1 65 + 1 3 + 1 13 = 65 = 60 2 4 12

= (98 +1) 98 2 = 4851 = (89 +1) 89 1 = 4005

1 6 + 12 1 1 1 1 1 715 143 1 143 25 + + + + = = = 7 8 4 20 5 840 168 168 168 30 +120 + 300 + 50 = 500 25 500 = 3360 50 168

1 3 1 1 1 1 ( ) = 3 4 6 1 1 1 1 1 ( ) = 3 6 5 10 1 1 1 3 + + = 3 6 10 5 3 5 240= 240= 400 400 5 3

3 + 1+ 2 = 4 2 5 5 1 4 2 1 5 1 4 2 22 5 = 1 = ( ) 5 5 22 5 22

5 22 1 1 1 3 1 5 1 1 1 = 1 2 2 3 5 5 1 1 1 1 +1+ 5 23 = 1 = 6 2 3 2 6 23

1 8 1 x 2 x 8 8 x 2 + 12 = x 8 x 2 + 12 = x 8

2 x = 64 64 4768 2 6432 = 2

0 1 2 3 4 5 6 7 8 9 10 0 1 10 11 100 101 110 111 1000 1001 1010

xyz = 32118 x 4 40 < y 79

S DEF = 1 2 ah S S S S DEF DOE EOF FOD 1 aoa + OB + OC 2 1 S DEFah 2 S +S S = 1 2 a h h + h DO E DOF EOF 1 2 3 1 ah = 1 2 a h 1 + h 2 + h 3 2

x x 4 x 2 x + 4 x + 6 + 3 + 1 = x 2 2 x = y x y 1 2 2 y 4y + 10 y 2 2 y - 8y - 20 = 0 y 10 y = -2 1 2

lg 5x + 5 = 1 1 lg( 2x 1); 2 S = s( s a)( s b)( s c). 1g 5x + 5 =1-1 lg 2x -1 2

1 lg2x -1 = lg 2x -1 2 lg 5x + 5 = lg10 lg 2x 1, lg 5x + 5 + lg 2x 1 = lg 10, lg ( 5x + 5)( 2x 1) = lg 10, ( 5x + 5)( 2x 1) = 10 ( 5x + 5)( 2x 1= 100 2 2x + x - 21 = 0 x = 3 x = - 7 1 2 2 = lg 5x + 5 = lg 5 3 + 5 = lg 20 = 1 1 + lg2 2 = 1-1 2 lg 2x -1 = 1-1 lg 2 3-1 2 = 1-1 2 lg5 = 1-1 lg10 - lg2 2 = 1 2 + 1 2 lg2 = 1 1+ lg2 2

x = - 7 2 2 = lg 5 (- 7 25 ) + 5 = lg 2 2 x = - 7 2 ( x 1) x x = x

CF CA = CB CF 2 2 5 + 1 2 F(n) = 2 n +1

2 F(0) = 2 +1= 2 +1= 3 2 0 1 F(1) = 2 +1= 4 +1= 5 22 F(2) = 2 +1 = 16 +1= 17 23 F(3) = 2 +1= 256 +1 = 257 2 F(4) = 2 4 +1= 65536 +1 = 65537

x 2 x 5 z 5 x x x + + + 6 + 4x 2 5 5 x = 10 10 x 100

n 1 n 2 5 n = 5 5 1 5 2 65 2 2