1. .
2. .
3. .
4. .
, - , .
: , .
, , , . , , .
, ( ), .
n :
= ( - 1)( - 2}...[ - ( - 1)]. (1)
1.
:
1) 10 4;
2) ( +4) ( 2).
1) = 10∙9∙8∙7 = 5040;
2) = (n + 4)(n + 3)[ n + 4 (n 2 - 1)] = (n + 4)(n + 3)8∙7.
2.
= 30 .
: n 5, n 5, n 5,
n 2 4; n 2 + 4; n 6.
= n (n 1)(n 2)(n 3)(n 4)
= (n 2)(n 3)(n 4)(n 5)
n (n 1)(n 2)(n 3)(n 4) = (n 2)(n 3)(n 4)(n 5);
n (n 1) = 30(n 5);
n 2 31 n + 150 = 0;
n 1=6, n 2=25.
: n 1=6, n 2=25.
3.
:
1) 5! + 6!;
2) ;
1) 5! + 6! = 5∙4∙3∙2∙1 + 6∙5∙4∙3∙2∙1 = 120 + 720 = 840;
2) = = 52∙51 = 2652.
, .
. , . .
= = ( - 1)( - 2)...3.2.1 = 12∙3...( - 1) (2)
1 . 123... ( 1) ! ( -), 0! = 1, 1! = 1. (2)
= ! (3)
(3), (1)
= = (4)
=(n - m) (5)
4.
:
1) 1;
2) 5, 6;
3) a, b, c.
1) 1 = 1 (1);
2) 2 = 1∙2 (5,6), (6,5);
3) 3 = 1∙2∙3 = 6 (a,b,c), (a,c,b), (b,a,c), (c,a,b), (c,b,a), (b,c,a),
, .
.
|
|
= (6)
= (7)
= (8)
, , :
= (0 m n) (9)
( = 1 = 1);
+ = (10)
5.
:
1) ;
2) + .
1) = = = 15∙7 = 105;
2) + = +1 = +1 = 15 + 1 = 16.
6.
= ,
= 66.
: 2, ( 2- )
= 66,
= 66,
x 2 x 132 = 0,
x 1 = - 11 ( ), x 2 = 12.
= 12 ,
= , (9), =
= ,
12 y = y + 2,
y = 12, y = 5.
: y = 12, y = 5.
1. : 1) , 2) .
2. :
1) + + ; 2) ; 3) .
3. 30 . ?
4. ?
5. :
1) = 42 ; 2) = ; 3) = 5 m (m + 1); 4) = 13; 5) = 14 ;
6) = 4 ; 7) 20 = ; 8) = 15 .
6. C : a, b, c, d.
7. :
1) ; 2) ; 3) 6!(7! 3!).
8. :
1) = (m + 1)(m + 2)(m + 3)(m + 4);
2) = (n - 2)(n - 3).
9. :
1) ; 2) ; 3) .
10. :
1) + ; 2) - ;
3) .
11. 10 ?
12. 12 12 ?
13. 1, 2, 3, 4, 5 ?
14. 7 7 ?
15. :
1) ; 2) ; 3) ; 4) + .
16. :
1) = ;
2) = ;
3) + = ;
4) + = ;
5) = ;
6) - = .