La règle de d'Alembert

Soit la suite de terme général $a_n={\dfrac{n-2}{(n+1)!}}$a, start subscript, n, end subscript, equals, start fraction, n, minus, 2, divided by, left parenthesis, n, plus, 1, right parenthesis, !, end fraction.

$\displaystyle\lim_{n\to+\infty}\left|\, \frac{{{a}_{n+1}}}{{{a}_{n}}} \,\right|=$limit, start subscript, n, \to, plus, infinity, end subscript, open vertical bar, start fraction, a, start subscript, n, plus, 1, end subscript, divided by, a, start subscript, n, end subscript, end fraction, close vertical bar, equals