, ᒺ , .
: () (, , ).
: ( ).
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= *
= *
= *.
. , . , .
: - reserve, ; reservere . . -, , . . -, . .
쳿 .
IV. .
, ( ) ᒺ . , .
() ().
|
|
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.
:
1. :
Y = 1 + 2 + 3 +...+ n
, .
2. :
Y = 1 * 2 * 3 *...* n
, .
3. :
Y = 1 / 2
, .
4 () .
. , :
= * ;
= * * ;
= * * * .
ֳ .
.
: , , .
. , () : () ():
= /
( (), (), (), (), ()), :
= / + / + / + / + /.
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= /
= /(++++)
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= /
= * /* = / * / = * ,
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. , () () (). , : () ().
|
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= : / : = /.
V. .
, , , .
, , . , . .
:
- ;
- ;
- ;
- .
, . ³ . , , . () , , . , , .
, , = 1 23, (0) (1) :
0 = 10 2030;
1 = 11 2131.
, , :
: 0 = 10 2030;
1- ( ): 1 = 11 2030;
2- ( ): 2 = 11 2130;
( ): 1 = 11 2131;
, :
1 : ∆1 = 11 2030 - 10 2030 = 1 - 0;
2 : ∆2 = 11 2130 - 11 2030 = 2 1;
3 : ∆3 = 11 2131 - 11 2130 = 1 2.
∆ = 1 - 0 = ∆1 + ∆2 + ∆3.
.
| 1 | 2 | 3 | |||
| 10 | 20 | 30 | 0 | - | |
| 11 | 20 | 30 | 1 | ∆1 = 1 - 0 | |
| 11 | 21 | 30 | 2 | ∆2 = 2 1 | |
| 3 () | 11 | 21 | 31 | 1 | ∆3 = 1 2 |
.
() (), () ().
=
.
.
| ³, (+,-) | ||||
| ³, % | ||||
| 1. , | 36562,5 | +4082,5 | +12,569 | |
| 2. , . | +7 | +12, 069 | ||
| 3. | +5 | +7,143 | ||
| 4. , | 7,5 | -0,5 | -6,25 |
|
|
|
-
| - | |||||
| ∆ = 36400 32480 = +3920 | |||||
| ∆ = 39000 36400 = +2600 | |||||
| 3 () | 7,5 | 36562,5 | ∆ = 36562,5 39000 = -2437,5 |
: ∆ = ∆ + ∆ + ∆ = 3920 + 2600 - 2437,5 = 4082,5.
:
- 4082,5 ;
- 7 3920 ;
- 5 2600 ;
- 0,5 , 2437,5 .
, .
() , , .
, .
.
, , , , .
= 1 23 .
∆1 = ∆ 1 2030;
∆2 = 11 ∆230;
∆3 = 11 21∆3.
, , .
∆ = ∆ 0 0 = 7 70 8 = 3920;
∆ = 1 ∆ 0 = 65 5 8 = 2600;
∆ = 1 1∆ = 65 75 (-0,5) = -2437,5.
( ).
. ³ , , .
= 1 23 .
:
∆% = 
:
∆1 = 
;
∆2 = 
;
∆3 = 
.
( ) :
|
|
|
∆ = 
= 
= 3920;
∆ = 
= 
= 2600;
∆ = 
= = 
= - 2437,5.
( , - ).
, , . ᒺ , () .
() :
= 
,
q1 q0 , 1 0 .
:
= 
, .
() . :
) :
q = 
г :
q = 
) :
= 
:
= 
() , () .
:
= q ;
= q + .
: 305 3 325 6 ; 250 4 360 5 . .
| q1p0 | |||||||
| q0, | p0, | q0p0, | q1, | p1, | q1p1, | ||
, , :
= 
= 1,023 (102,3%); = 2865 2800 = 65;
q = 
= 1,016 (101,6%); q = 2845 2800 = 45;
= 
= 1,007 (100,7%); = 2865 2845 = 20.
= q = 1,016 1,007 = 1,023; = q + = 65 + 45 = 20.
:
- 2,3% ( 65 );
- 1,6%, 45 ;
- 0,7% 20 .
V. , .
, , . , , . , .
= 1 2 :
∆1 = 
∆ 1 (20 + 21);
∆2 = ∆2 (10 + 11).
, , :
| () | + 5050 | ||
| () | - 200 | ||
| () | 2,1 | +0,1 |
= ;
∆ = ∆ ( 0 + 1) = (-200) (2 + 2,1) = - 410;
∆ = ∆ ( 0 + 1) = 0,1 (54700 + 54500) = 5460.
5050 , 410 , 5460 .
|
|
|
:
= 1 23;
∆1 = ∆ 1 (2031 + 2130) + 
∆1∆ 2∆3;
∆2 = ∆ 2 (1031 + 1130) + ∆1 ∆2∆3;
∆3 = ∆ 3 (1021 + 1120) + ∆1 ∆2∆3 .
:
| () | +2446 | ||
| () | +12 | ||
| () | -10 | ||
| () | 0,35 | 0,4 | +0,05 |
= ;
∆ = ∆ (0 1 + 1 0) + ∆ ∆ ∆ =
= 12 (280 0,4 + 270 0,35) + 12 (-10) 0,05 = 1237;
∆ = ∆ (0 1 + 1 0) + ∆ ∆ ∆ =
= (-10) (115 0,4 + 127 0,35) + 12 (-10) 0,05 = - 454,25;
∆ = ∆ (0 1 + 1 0) + ∆ ∆ ∆ =
= 0,05 (115 270 + 127 280) + 12 (-10) 0,05 = 1663,25.
:
- , 1237 ;
- 1663,25 .
454,25 .
. ³ Y = 1 + 2 + 3 +...+ n
Y = 
.
:
∆2 = 
∆2;
∆3 = ∆3;
∆4 = ∆4.
, () 20%, , .
| () | -800 | ||
| () | +100 | ||
| () | -600 | ||
| () | +300 | ||
| -1000 |
= 
= 
, -
∆ = 
∆ = 
(-800) = 16%;
∆ = ∆ = 100 = - 2%;
∆ = ∆ = (-600) = 12%;
∆ = ∆ = 300 = - 6%.
∆ = 16 2 12 6 = 20%
16 12 . ( 2 6% ) .
, . , .
= 1 23
∆1 = 
∆;
∆2 = ∆;
∆3 = ∆.
= :
∆ = 
∆ = 
2446 =14318,05;
∆ = 
∆ = 
2446 = - 11931,71;
∆ = 
∆ = 
2446 = 59,66.
∆ = 14318,05 - 11931,71 + 59,66 = 2446.
, , , .
V. .
. , , . . :
1. .
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2. .
:
- ;
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:
max Kj = 
,
Kj j- ᒺ ();
j ( ) - j- ;
n .
:
min Kj =
| 1- | 2- | 3- | |||||||
| % .. | % .. | % .. | |||||||
| 1) , % | 4,2 | 4,85 | |||||||
| 2) , . | 100,125 | 100,392 | 108,108 | ||||||
| 3) | - | - | 99,1 | - | - | 99,5 | - | - | 99,7 |
| 4) , . | 100,16 | 100,36 | 100,645 |
, .
| % | |||
| 1- | 2- | 3- | |
| 1) , % | |||
| 2) , . | 100,125 | 100,392 | 108,108 |
| 3) | 99,1 | 99,5 | 99,7 |
| 4) , . | 100,16 | 100,36 | 100,645 |
| 404,385 | 400, 252 | 405,445 | |
| ̳ |
2. ( ) ᒺ . j sj, ᒺ - . (sj), :
Kj = 
ᒺ min Kj.
| 1- | 2- | 3- | |
| 1) , % | |||
| 2) , . | |||
| 3) | |||
| 4) , . | |||
| 10 | 8 | 6 | |
| ̳ |
3. . ᒺ ᒺ-. :
Kj = 
0j - .
ᒺ min Kj.
. , . .
| 1- | 2- | 3- | ||
| 1) , % | ||||
| 2) , . | 108,108 | 59,29 | ||
| 3) | 99,7 | 0,36 | 0,04 | |
| 4) , . | 100,645 | 0,16 | 0,04 | |
| 64,52 | 84,37 | 64 | ||
| ̳ |
