$(n+2)!(n+3-1)=42n!(n+1+1)$
$(n+2)(n+1).n!.(n+2)=42.n!(n+2)$
$n+2)(n+1)=42$
$n=5$ dir.
$$(n+3)(n+2)(n+1)n!-(n+2)(n+1)n!=42n![(n+1)+1]$$
$$\Rightarrow$$
$$(n+3)(n+2)(n+1)-(n+2)(n+1)=42[(n+1)+1]$$
$$(n+2)(n+1)[(n+3)-1)]=42(n+2)$$
$$(n+2)(n+1)=42$$
$$n=\ldots $$