Question

решить неравинство (n+4)!/(n+2)! ≤ 56

Answer 1

$\frac{(n+4)!}{(n+2)!} \leq 56; (n+3)(n+4) \leq 56;$
решаю методом интервалов:
(n+3)(n+4)=56
$n^{2} +7n+12-56=0; n^{2}+7n-44=0; \left \{ {{ n_{1}*n_{2}=44} \atop {n_{1}+n_{2}=-7}} \right. ; \left \{ {{ n_{1}=-11} \atop {n_{2}=4}} \right.;$
n ∈ [-11;4]
Ответ: [-11;4]