Найдите значение выражения:1)13!/7!*6!2)4!*5!/10!3)5!*8!/10!*2!. Created by aleksandra2022. algebra-ru

10!*2!...

aleksandra2022 @aleksandra2022

July 2022 1 8 Report

Найдите значение выражения:
1)13!/7!*6!
2)4!*5!/10!
3)5!*8!/10!*2!

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Ответ:

n! = 1·2·3·...·(n-1)·n - факториал.

$1)\ \dfrac{13!}{7!*6!} = \dfrac{1*2*3*4*5*6*7*8*9*10*11*12*13}{1*2*3*4*5*6*7*6!} = \\\\= \dfrac{8*9*10*11*12*13}{6!} = \dfrac{8*9*10*11*12*13}{1*2*3*4*5*6} = \\\\= \dfrac{2*4*3*3*2*5*11*12*13}{1*2*3*4*5*6} = \dfrac{11*12*13}{1} = 11*12*13 = 1716$

$2)\ \dfrac{4!*5!}{10!} = \dfrac{4!*1*2*3*4*5}{1*2*3*4*5*6*7*8*9*10} = \\\\= \dfrac{4!}{6*7*8*9*10} = \dfrac{1*2*3*4}{2*3*7*2*4*9*10} = \\\\= \dfrac{1}{7*2*9*10} = \dfrac{1}{1260}$

$3)\ \dfrac{5!*8!}{10!*2!} = \dfrac{5!*1*2*3*4*5*6*7*8}{1*2*3*4*5*6*7*8*9*10*2!} = \\\\= \dfrac{5!}{9*10*2!} = \dfrac{1*2*3*4*5}{9*10*2} = \\\\= \dfrac{2*3*20}{3*3*20} = \dfrac{2}{3}$

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na koren iz 7

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