Решение.
Формулы: [tex]\bf n!=1\cdot 2\cdot 3\cdot ,,,\cdot (n-1)\cdot n=(n-1)!\cdot n\ \ ,[/tex]
[tex]\bf n!=(n-2)!\cdot (n-1)\cdot n[/tex]
[tex]\displaystyle \bf 1)\ \ \frac{5!+6!+7!}{8!-7!}=\frac{5!+5!\cdot 6+5!\cdot 6\cdot 7}{7!\cdot 8-7!}=\frac{5!\cdot (1+6+6\cdot 7)}{7!\cdot (8-1)}=\\\\\\=\frac{5!\cdot (1+6+42)}{5!\cdot 6\cdot 7\cdot 7}=\frac{49}{6\cdot 7\cdot 7}=\frac{1}{6}[/tex]
[tex]\displaystyle \bf 2)\ \ \frac{18!-17\cdot 17!-16\cdot 16!}{17!-16!}= \frac{16!\cdot 17\cdot 18-17\cdot 16!\cdot 17-16\cdot 16!}{16!\cdot 17-16!}=\\\\\\=\frac{16!\cdot (17\cdot 18-17\cdot 17-16)}{16!\cdot (17-1)}=\frac{17-16}{16}=\frac{1}{16}=0,0625[/tex]
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Answers & Comments
Решение.
Формулы: [tex]\bf n!=1\cdot 2\cdot 3\cdot ,,,\cdot (n-1)\cdot n=(n-1)!\cdot n\ \ ,[/tex]
[tex]\bf n!=(n-2)!\cdot (n-1)\cdot n[/tex]
[tex]\displaystyle \bf 1)\ \ \frac{5!+6!+7!}{8!-7!}=\frac{5!+5!\cdot 6+5!\cdot 6\cdot 7}{7!\cdot 8-7!}=\frac{5!\cdot (1+6+6\cdot 7)}{7!\cdot (8-1)}=\\\\\\=\frac{5!\cdot (1+6+42)}{5!\cdot 6\cdot 7\cdot 7}=\frac{49}{6\cdot 7\cdot 7}=\frac{1}{6}[/tex]
[tex]\displaystyle \bf 2)\ \ \frac{18!-17\cdot 17!-16\cdot 16!}{17!-16!}= \frac{16!\cdot 17\cdot 18-17\cdot 16!\cdot 17-16\cdot 16!}{16!\cdot 17-16!}=\\\\\\=\frac{16!\cdot (17\cdot 18-17\cdot 17-16)}{16!\cdot (17-1)}=\frac{17-16}{16}=\frac{1}{16}=0,0625[/tex]