помогите с факториалами 1) 6!-4!/3! 2 ) 5!/3!+4! 3) 5!*3!/6. Created by nivle10. matematika-ru

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nivle10 @nivle10

March 2022 1 10 Report

помогите с факториалами
1) 6!-4!/3!
2 ) 5!/3!+4!
3) 5!*3!/6

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NNNLLL54

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$n!=1\cdot 2\cdot 3\cdot 4\cdot \ldots \cdot (n-1)\cdot n\; \; \; \Rightarrow \; \; \; n!=(n-1)!\cdot n\\\\1)\; \; 4!=1\cdot 2\cdot 3\cdot 4\\\\6!=1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6=(1\cdot 2\cdot 3\cdot 4)\cdot 5\cdot 6=4!\cdot 5\cdot 6\\\\ \frac{6!-4!}{3!}= \frac{4!\cdot 5\cdot 6\, -\, 4!}{3!} = \frac{4!\, (5\cdot 6\, -1)}{3!}=[\, 4!=3!\cdot 4\, ]= \frac{3!\cdot 4\cdot 29}{3!} =4\cdot 29=116$

$2)\; \; \frac{5!}{3!+4!} = \frac{3!\cdot 4\,\cdot 5}{3!+3!\cdot 4} = \frac{3!\cdot 4\, \cdot 5}{3!(1+4)} = \frac{20}{5} =4\\\\3)\quad \frac{5!\cdot \, 3!}{6} = \frac{1\cdot 2\cdot 3\cdot 4\cdot 5\; \cdot \; 1\cdot 2\cdot 3}{6} = 1\cdot 2\cdot 3\cdot 4\cdot 5 =120$

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