Question

fatorial

determine o conjunto dos valores de n tais que :

$\frac{n!+(n+1)!}{(n-1)!} =15$

Answer 1

Delícia de questão <3

$\dfrac{n!+(n+1)!}{(n-1)!}=15$

$n!=n(n-1)!$

$(n+1)!=(n+1)n(n-1)!$

$\dfrac{(n-1)![n+n(n+1)]}{(n-1)!}=15$

$n+n(n+1)=15$

$n+n^2+n=15$

$n^2+2n-15=0$

$\Delta=2^2-4\cdot1\cdot(-15)=4+60=64$

$n=\dfrac{-2\pm\sqrt{64}}{2}$

$n>0$

$n=\dfrac{-2+8}{2}=\dfrac{6}{2}=3$

$S=\{3\}$