Question

помогите пожалуйста решить

Answer 1

$lim_{n to infty} frac{(n+4)!-(n+2)!}{(n+3)!} = {{ frac{ infty- infty}{ infty} } }= lim_{n to infty} frac{(n+2)!(n+3)(n+4)-(n+2)!}{(n+2)!(n+3)} = \ \ = lim_{n to infty} frac{(n+2)!((n+3)(n+4)-1)}{(n+2)!(n+3)}= lim_{n to infty} frac{n^2+7n+12-1}{n+3} = \ \ = lim_{n to infty} frac{n^2+7n+11}{0n^2+n+3} = frac{1}{0} = infty$