1)1051,68
2)1608
3)0,84
4)372,38
5)163,989
6)233,49
А)1/10 *3=3/10
б)1/8*3=3/8
в)1/5*5=5/5=1
г)1/5*15=15/5=3
д)2*1/7*3=1/7*6=6/7
е)1/17*23*2=1/17*46=46/17=2 целых и 12/17
ё)1/9*3=3/9=1/3
ж)1/16*16=16/16=1
|x-15|=15-x
x>=15
x-15=15-x
x=15
x<15
15-x=15-x
0=0
ответ x<=15
Вспоминаем, что такое факториал.
(3n-1)! = 1*2*3*...*(3n-1)
(3n+1)! = 1*2*3*...*(3n-1)*3n*(3n+1)
(3n)! = 1*2*3*...*(3n-1)*3n = (3n-1)! * 3n
В числителе вынесем за скобки
(3n-1)! + (3n+1)! = 1*2*3*...*(3n-1) + 1*2*3*...*(3n-1)*3n*(3n+1) =
= 1*2*3*...*(3n-1) * (1 + 3n*(3n+1)) = (3n-1)! * (9n² + 3n + 1)
Подставляем
![\lim_{n \to \infty} \frac{(3n-1)!+(3n+1)!}{(3n)! (n-1)} =\lim_{n \to \infty} \frac{(3n-1)! * (9 n^{2} + 3n + 1)}{(3n-1)! * 3n(n-1)} =](https://tex.z-dn.net/?f=+%5Clim_%7Bn+%5Cto+%5Cinfty%7D++%5Cfrac%7B%283n-1%29%21%2B%283n%2B1%29%21%7D%7B%283n%29%21+%28n-1%29%7D+%3D%5Clim_%7Bn+%5Cto+%5Cinfty%7D++%5Cfrac%7B%283n-1%29%21+%2A+%289+n%5E%7B2%7D++%2B+3n+%2B+1%29%7D%7B%283n-1%29%21+%2A+3n%28n-1%29%7D+%3D)
![=\lim_{n \to \infty} \frac{9 n^{2} + 3n + 1}{3n(n-1)} =\lim_{n \to \infty} \frac{9 n^{2} + 3n + 1}{3 n^{2} -3n} =](https://tex.z-dn.net/?f=%3D%5Clim_%7Bn+%5Cto+%5Cinfty%7D++%5Cfrac%7B9+n%5E%7B2%7D++%2B+3n+%2B+1%7D%7B3n%28n-1%29%7D+%3D%5Clim_%7Bn+%5Cto+%5Cinfty%7D++%5Cfrac%7B9+n%5E%7B2%7D++%2B+3n+%2B+1%7D%7B3+n%5E%7B2%7D+-3n%7D+%3D)
Разделим числитель и знаменатель на n²
![=\lim_{n \to \infty} \frac{9 + \frac{3}{n} + \frac{1}{ n^{2} } }{3- \frac{3}{n}} =\frac{9 + \frac{3}{oo} + \frac{1}{ oo^{2} } }{3- \frac{3}{oo}} = \frac{9+0+0}{3-0} = \frac{9}{3} =3](https://tex.z-dn.net/?f=%3D%5Clim_%7Bn+%5Cto+%5Cinfty%7D++%5Cfrac%7B9+%2B+%5Cfrac%7B3%7D%7Bn%7D+%2B++%5Cfrac%7B1%7D%7B+n%5E%7B2%7D+%7D+%7D%7B3-+%5Cfrac%7B3%7D%7Bn%7D%7D+%3D%5Cfrac%7B9+%2B+%5Cfrac%7B3%7D%7Boo%7D+%2B++%5Cfrac%7B1%7D%7B+oo%5E%7B2%7D+%7D+%7D%7B3-+%5Cfrac%7B3%7D%7Boo%7D%7D+%3D+%5Cfrac%7B9%2B0%2B0%7D%7B3-0%7D+%3D+%5Cfrac%7B9%7D%7B3%7D+%3D3)
5*4=20 ( тг ) - стоимость 4 шт.