Question

Найдите предел функции
$lim_{n to infty} frac{(n+4)!-(n+2)!}{(n+3)!}$

Answer 1

[(n+1)!-(n+2)!]/(n+3)!=(n+1)!(1-n-2)/[(n+1)!*(n+2)*(n+3)]=
=-(n+1)/(n²+5n+6)
lim[n²(-1/n-1/n²)]/[n²(1+5/n+6/n²)]=lim(-1/n-1/n²)/(1+5/n+6/n²)=(-0-0)/(1+0+0)=0