Question

Calcule

A) 15!/14!

B) 11! - 9!/8!

C) 700×48!/50!

D) 99!×98!/100!×97

C)(n+2)!-(n+1)!/(n²+n)(n-1)!

Answer 1

Resposta:

Explicação passo-a-passo:

19.1.

$a)\\\\\dfrac{15!}{14!}=\dfrac{15.14!}{14!}=15\\\\\\b)\\\\\dfrac{11!-9!}{8!}=\dfrac{11.10.9.8!-9.8!}{8!}=\dfrac{(11.10.9-9).8!}{8!}=11.10.9-9=990-9=981\\\\c)\\\\\dfrac{700.48!}{50!}=\dfrac{700.48!}{50.49.48!}=\dfrac{700}{50.49}=\dfrac{7.2.5}{5.7.7}=\dfrac{2}{7}\\\\d)\\\\\dfrac{99!98!}{100!97!}=\dfrac{99!98.97!}{100.99!97!}=\dfrac{98}{100}=\dfrac{49}{50}\\\\19.2\\\\\dfrac{(n+2)!-(n+1)!}{(n^{2}+n)(n-1)!}=\dfrac{(n+2)(n-1)!-(n+1)!}{n(n+1)(n-1)!}=$

$=\dfrac{[(n+2)-1](n-1)!}{n(n+1)(n-1)!}=\dfrac{[n+2-1]}{n(n+1)}=\dfrac{[n+1]}{n(n+1)}=\dfrac{1}{n}$