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F M B N
{1, 2, 3, 4, 5}
{1, 3, 6,10,15}

F M B N
1, 3, 5, 7, 9,..., 2 1n
1 2 3 4 5 ...
...1 3 5 7 9
{1, 2, 3, 4, 5,...}
{1, 3, 5, 7, 9,...}

F M B N
n
( )f x 1x
( )1f 1 1 2
( )2f 2 1 3
( )3f 3 1 4
( )4f 4 1 5
2, 3, 4, 5
1, 2, 3, 4
( ) 1f x x ( )f x x
1, 2, 3, 4( )f x x

F M B N
1
{1, 2, 3,..., }n
{1, 2, 3,...}

F M B N
a 1 2 3, , , ..., na a a a
a 1 2 3, , , ..., , ...na a a a
1a 1
2a 2
3a 3

na n

F M B N
2, 4, 6, 8,10
1a
2a
3a
2
4
6
4a
5a
na
8
10
2n
3, 4, 5, 6, 7,...
1a
2a
3a
3
4
5
4a
5a
na
6
7
2n

F M B N
2, 4, 6, 8,10
3, 4, 5, 6, 7,...
2, 4, 6, 8,10 2n {1, 2, 3, 4, 5}n
3, 4, 5, 6, 7, ... 2n n I

F M B N
4, 8,12,16, 20
2
1, 4, 9,16, 25, ..., , ...n
2 1 ; {1, 2, 3, 4, 5, ...,10}na n n
( 1)
2
n
n n
a
2
na n n

F M B N
n
2 1na n
na 2 1n
1a 2(1) 1 3
2a 2(2) 1 5
3a 2(3) 1 7
4a 2(4) 1 9
3, 5, 7, 9

F M B N
n
( 1) 2n
na
na ( 1) 2n
1a 1
( 1) 2 ( 1) 2
2a 2
( 1) 2 1 2
3a 3
( 1) 2 ( 1) 2
4a 4
( 1) 2 1 2
1, 3,1, 3
1
3
1
3

F M B N
n
2 1n
na
na 2 1n
1a 1
2 1 2 1
2a 2
2 1 4 1
3a 3
2 1 8 1
4a 4
2 1 16 1
3, 5, 9,17, ..., 2 1, ...n
3
5
9
17

F M B N
n
3, 7,11,15, ...
3 7 11 15
19
4 4 4
19 23
4 4
23

F M B N
n
30, 27, 24, 20,...
30 27 24 20
16
3 3 3
16 12
3 3
12

F M B N
n
4, 8,16, 32, ...
4 8 16 32
64
2 2 2
64 128
2 2
128

F M B N
n
243, 81, 27, 9, ...
243 81 27 9
3
3 3 3
3 1
3 3
1

F M B N
n
2, 3, 5, 8, ...
2 3 5 8
12
1 2 3
12 17
4 5
17

F M B N
n
100, 98, 94, 88, ...
100 98 94 88
80
2 4 6
80 70
8 10
70

F M B N
2, 4, 6, 8,10
2na n
1a
2a
3a
2
4
6 na 2
2, 4, 6, 8,10
2 2
2 3
2 1
n
4a
5a
8
10
2 4
2 5
{1, 2, 3, 4, 5}n

F M B N
4, 5, 6, 7, 8
3na n
1a
2a
3a
4
5
6 na
4, 5, 6, 7, 8
2
3
1 4a
5a
7
8
4
5
{1, 2, 3, 4, 5}n
3
3
3
3
3
n 3

F M B N
1, 3, 5, 7, 9
2 1na n
1a
2a
3a
1
3
5 na
1, 3, 5, 7, 9
2
3
1 4a
5a
7
9
4
5
{1, 2, 3, 4, 5}n
1
2
3
4
n ( 1)n
2 1n

F M B N
1, 2, 3, 4, 5
( 1)n
na n
1a
2a
3a
1
2
3 na
1, 2, 3, 4, 5
2
3
1 4a
5a
4
5
4
5
{1, 2, 3, 4, 5}n
n ( 1)
( 1)n
n
( 1)
( 1)
( 1)
( 1)
( 1)
1
2
3
4
5
n

F M B N
1, 2, 3, 2, 5
na n
1a
2a
3a
1
2
3 na
1, 2, 3, 2, 5
2
3
1 4a
5a
2
5
4
5
{1, 2, 3, 4, 5}n
n

F M B N
3 4 5 6 7
, , , ,
5 6 7 8 9
2
4
n
n
a
n
{1, 2, 3, 4, 5}n
3 4 5 6 7
5 6 7 8 9
1 2 3 4 52 2 2 2 2
1 2 3 4 54 4 4 4 4
... n 2
... n 4
2
4
n
n

F M B N
2 , 4 , 6 , 8 , 10
10 , 15 , 20 , 25 , 30
8 , 16 , 24 , 32 , 40
2 2 2 2
5 5 5 5
8 8 8 8

F M B N
3, 6, 9,12,15
6 3 3
9 6 3
12 9 3
15 12 3
3

F M B N
1d 5 3 2
2d 7 5 2
3d 9 7 2
4d 11 9 2
3, 5, 7, 9,11
3, 5, 7, 9,11
2
d

F M B N
1d 17 ( 20) 3
2d 14 ( 17) 3
3d 11 ( 14) 3
4d 8 ( 11) 3
20, 17, 14, 11, 8
20, 17, 14, 11, 8
3
d

F M B N
1d 20 24 4
2d 16 20 4
3d 12 16 4
4d 8 12 4
24, 20,16,12, 8,...
24, 20,16,12, 8,...
-4
d

F M B N
1d 4 2 2
2d 8 4 4
3d 16 8 8
4d 32 16 16
2, 4, 8,16, 32,...
2, 4, 8,16, 32,...
d

F M B N
1 2 3 4 5, , , , , ..., , ...na a a a a a d
1a
2a 1a d
3a 2a d
4a 3a d
1( )a d d 1 2a d
1( 2 )a d d 1 3a d
5a 4a d 1( 3 )a d d 1 4a d
na 1 ( 1)a n d
 

F M B N
1 2 3 4 5, , , , , ..., , ...na a a a a a
d n
1 ( 1)na a n d
1

F M B N
4, 5, 6 7
5 3
1 5a 3d
na 1 ( 1)a n d
4a 5 ( )4 1 3 5 9 14
5a 5 ( )5 1 3 5 12 17
6a 5 ( )6 1 3 5 15 20
7a 5 ( )7 1 3 5 18 23
1 ( 1)na a n d

F M B N
4, 5, 6 7
5 3
1 5a 3d
na 1 ( 1)a n d
4a 5 ( )4 1 3 5 9 14
5a 4a d 14 3 17
6a 5a d 17 3 20
7a 6a d 20 3 23
1 ( 1)na a n d

F M B N
1 12a 17 12 5d
na 1 ( 1)a n d
6a 612 ( 1)5 12 25 37
7a 712 ( 1)5 12 30 42
8a 812 ( 1)5 12 35 47
9a 912 ( 1)5 12 40 52
12,17, 22, 27, 32,...
1 ( 1)na a n d

1 ( 1)na a n d
F M B N
1 12a 17 12 5d
na 1 ( 1)a n d
6a 612 ( 1)5 12 25 37
7a 6a d 37 5 42
8a 7a d 42 5 47
9a 8a d 47 5 52
12,17, 22, 27, 32,...

F M B N
35
1 4a 12 4 8d
na 1 ( 1)a n d
35a 354 ( 1)8 4 272 276
4,12, 20, 28, 36, ...
35 276

F M B N
1 20a 17 20 3d
na 1 ( 1)a n d
na 20 ( 1)( 3)n
20,17,14,11, 8,...
23 3na n
20 3 3n
23 3n

F M B N
5 8 34
52
5 34a 8 52a
na 1 ( 1)a n d
5a 1 4a d
8a 1 7a d
1 4a d 34
1 7a d 52
1
2
12
3d 18
d 6
1a 6d 1
1 64( )a 34
1a 10

F M B N
15 10 31
3
10 31a 3d
na 1 ( 1)a n d
15a 1 14a d
1 14(3)a
15 ?a
1 42a
1a
10a 1 9a d
31 1 9(3)a
1 27a
1a 31 27
4
4 42
15a 46

F M B N
8 4 18
4
4 18a 4d
na 1 ( 1)a n d
8a 1 7a d
1 7(4)a
8 ?a
1 28a
1a
4a 1 3a d
18 1 3(4)a
1 12a
1a 18 12
6
6 28
8a 34

F M B N
6 12 85
7
12 85a 7d
na 1 ( 1)a n d
6a 1 5a d
1 5(7)a
6 ?a
1 35a
1a
12a 1 11a d
85 1 11(7)a
1 77a
1a 85 77
8
8 35
6a 43

F M B N
1 ( 1)na a n d
2
1a1
d
1 2 3 4 5 6 7 8 9 10, , , , , , , , ,a a a a a a a a a a
d d d d d d d d d
d 2d 3d 4d 5dd2d3d

F M B N
1, ..., , ..., , ..., , ...k m na a a a
d
( )m ka a m k d
10 14 114 0 (14 1 )0a a d
15 8 18 5 (8 5)1a a d

F M B N
15 10 31
3
10 31a 3d
ma ( )k ma dk
15 ?a
15a 10 15( )10a d
31 5(3)
31 15
4615a

F M B N
4 18a 4d
ma ( )k ma dk
8 ?a
8a 4 8( )4a d
18 4(4)
18 16
348a
8 4 18
4

F M B N
12 85a 7d
ma ( )k ma dk
6 ?a
6a 12 6( )12a d
85 ( 6)(7)
85 42
436a
6 12 85
7

F M B N
1 4a 5 16a
ma ( )k ma dk
?d
5a 1 5( )1a d
4 4d
3d
4, , , ,16a b c, ,a b c
16
4d12
a 4 3 7
b 7 3 10
c 10 3 13

F M B N
1 10a 16 10 6d
10,16, 22, 28, ...64
na 64 ?n
na 1 ( 1)na d
64 10 ( 1)(6)n
10 6 6n
4 6n
60 6n
n 10
64 10

F M B N
100 – 999 12
12 108
12 996
108,120,132,144, ..., 996
1 108, 996na a 12d
na 1 ( 1)na d
996 108 ( 1)(12)n
108 12 12n
996 96 12n
900 12n
n 75

F M B N
2, 4, 8,16, 32,...
2
4
2
2
8
4
2
16
8
2
32
16
1, 3, 9, 27, 81, ...
3
3
1
3
9
3
3
27
9
3
81
27

F M B N
4,16, 64, 256,1024,...
16
4
64
16
256
64
1024
256
4

F M B N
1r 5 /1 5
2r 25/ 5 5
3r 125/ 25 5
4r 625/125 5
1, 5, 25,125, 625
1, 5, 25,125, 625
5
r

F M B N
1 2 3 4 5, , , , , ..., , ...na a a a a a r
2a 1a r
3a 2a r
4a 3a r
1( )a r r 2
1a r
1
2
( )a r r 3
1a r
na 1
1
n
a r
 
1 2 3 4 5, , , , , ... , , ...na a a a a a
r r r r r
5a 4a r 1
3
( )a r r 4
1a r

F M B N
1 2 3 4 5, , , , , ..., , ...na a a a a a
r n
1
1
n
na a r
1

F M B N
1
3
4
a 4r
1a
3
4
2a 1a r
3
4
4
3
3a 2a r 3 4 12
4a 3a r 12 4 48
3
, 3,12, 48
4

F M B N
7 4, 20, 100, …
1 4a
20
5
4
r 7 ?a
na 1
1
n
a r
7a 7 1
4(5)
6
4(5)
4(15,625)
62,5007a

F M B N
1 2 3 4 5 6 7 8 9 10, , , , , , , , ,a a a a a a a a a a
r
2
r
r r r r r r r r
r 3
r 4
r 5
r1
r2
r3
r

F M B N
1, ..., , ..., , ..., , ...k m na a a a
r
m k
m ka a r
10 14 10
10
14
14a a r
15 8 15
15
8
8a a r

F M B N
7 3 5
4
3 5a 4r 7 ?a
ma m k
ka r
7a 7 3
3a r
4
5(4)
5(256)
1,2807a

F M B N
8, 16, 32, 64, …
1 8a
16
2
8
r ?na
na 1
1
n
a r
na 1
8(2)n
3
2
3 1
2 n
2
2n
na
1
2n

F M B N
1 2 3 4 5, , , , , ..., na a a a a a
1 2 3 4 5 ... na a a a a a
1a
2a
1
3a
2

na
3
n

F M B N
1 2 3 4 5, , , , , ..., na a a a a a
n nS
1S 1a
2S 1 2a a
3S 1 2 3a a a
nS 1 2 3 ... na a a a


F M B N
n
1 2 3 4 5 15
1 2 3 4 5 6 7 8 9 10
10 9 8 7 6 5 4 3 2 1
x
x
1
2
11 11 11 11 11 11 11 11 11 11 2x
10 11 2x
10 11
2
x 55
1 2 3 4 5 6 7 8 9 10 55

F M B N
n
( 2)n x
x
( 1)n n1 2 3
( 2)n( 1)nn 123...
...
( 1)n ( 1)n ( 1)n ( 1)n ( 1)n... ( 1)n 2x
n
( 1)nn 2x
( 1)
2
n n
x1 2 3 ... n
( 1)
2
n n
1 2 3 ... n ?

F M B N
n
1 2 3 4 ... na a a a anS
1 2 3 ... na a a a
1 2 3, , , ..., na a a a d
1a 1[ ]a d 1[ 2 ]a d 1[ ( 1) ]a n d...1[ 3 ]a d
1 1 1 1 12 3 ... ( 1)a a d a d a d a n d
1 1 1 1 1[ ... ]a a a a a [ 2 3 ... ( 1) ]d d d n d
n
1na [1 2 3 ... ( 1)]n d

F M B N
n
nS 1na [1 2 3 ... ( 1)]n d
1na
( 1)
2
n n
d
( 1)
1 2 3 ...
2
n n
n
12
2
na ( 1)
2
n n
d
12 ( 1)
2
na n nd
1[2 ( 1) ]
2
n a n d
1[2 ( 1) ]
2
n
a n d

F M B N
n
nS 1[2 ( 1) ]
2
n
a n d
1 1[ ( 1) ]
2
n
a a n d
1[ ]
2
n
n
a a
1 2 3 ... na a a a
1[2 ( 1) ]
2
n
n
S a n d 1[ ]
2
n n
n
S a a
n

F M B N
n
20 4 + 6 + 8 + 10 + …
1 4a 26 4d
nS 1[2 ( 1) ]
2
n
a n d
20S [2( ) (
20
20 14 )( )]
2
2
10[8 38] 460
nS 1[ ]
2
n
n
a a

F M B N
n
5 + 10 + 15 + 20 + … + 150
1 4a 150na
nS 1[2 ( 1) ]
2
n
a n d
na 1 ( 1)a n d
nS 1[ ]
2
n
n
a a
150 5 ( 1)(5)n
10 5 5d
5 5 5n
150 5n
30 n

F M B N
n
5 + 10 + 15 + 20 + … + 150
1 5a 150na
nS 1[2 ( 1) ]
2
n
a n d
nS
nS 1[ ]
2
n
n
a a
10 5 5d
(15)(155)nS
2,325
1[ ]
2
n
n
a a
30
[5 150]
2

F M B N
n
10 200
1 10a , 200na
nS 10 12 14 ... 200
nS 1[ ]
2
n
n
a a
12 10 2d
n
na 1 ( 1)a n d
200 10 ( 1)(2)n
10 2 2n
200 8 2n
192 2n
96 n

F M B N
n
10 200
1 10a , 200na
nS 10 12 14 ... 200
nS 1[ ]
2
n
n
a a
12 10 2d
n
200S
96
[10 200]
2
48(210) 10,080

F M B N
n
20 1 4
2 6 3 8
1a
d


F M B N
n
20 1 4
2 6 3 8
nS 1[2 ( 1) ]
2
n
a n d
[2( ) (
20
20 14 )( )]
2
2
10(8 38) 460
460

F M B N
n
1 2 4 8 16 31
1 2 4 8 16 32 64 128 256 512
2 4 8 16 32 64 128 256 512 1024
x
2x
; 2r
1024 1 x
1023 x
1 2 4 8 16 32 64 128 256 512 1023

F M B N
n
1 2 3 4 ... na a a a anS
1 2 3 4 ... na a a a a
1 2 3, , , ..., na a a a
r
2 3 1
1 1 1 1 1... n
a a r a r a r a r
2 3 1
1 1 1 1 1... n n
a r a r a r a r a rnrS
nS 1
2
12
n nrS S 1 1
n
a r a

F M B N
n
n nrS S 1 1
n
a r a
nS 1( 1)
1
n
a r
r
( 1) nr S 1( 1)n
a r
1(1 )
1
n
a r
r
nS
1r
1r
1 1
1
n
a a r
r
1
1 1
1
n
a a r r
r
1
1
na a r
rnS 1r

F M B N
n
1 2 3 ... na a a a
n
r
1(1 )
1
n
n
a r
S
r
1r
1
1
n
n
a a r
S
r
1r

F M B N
n
1 + 2 + 4 + 8 + 16 + … + 2048
1 1a
2
2
1
r
nS 1(1 )
1
n
a r
r
20S
4095
nS 1
1
na a r
r
2048na
1 2048(2)
1 2
1 4096
1 2
4095
1

F M B N
n
4
1 3a 4n
nS 1(1 )
1
n
a r
r
4S
45
nS 1
1
na a r
r
2r
4
3(1 2 )
1 2
3(1 16)
1 2
45
1
1 3, 2a r

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