Question

`lim_(x->oo) ((n+2)!+(n+1)!)/((n+2)!+(n+1)!)` ?

Answer 1

Answer `=1`

Explanation:

Let's first consider what is being asked in the question.

Answer `=lim_(x->oo) ((n+2)!+(n+1)!)/((n+2)!+(n+1)!)`

Now we have a couple of things to mention:

(i) `x` is not involved in the limit. We could assume that `x` was supposed to have been `n`.

(ii) Since the numerator and the denominator are equal for all `n`, the object of our limit equals `1`.

`:. lim_(n->oo) ((n+2)!+(n+1)!)/((n+2)!+(n+1)!) = 1`

Hence, Answer `=1`

BTW: If the question was meant to be:

Answer `=lim_(n->oo) (n+2)!+((n+1)!)/((n+2)!)+(n+1)!`

`= lim_(n->oo) (n+2)! + 1/(n+2) + (n+1)!`

`= oo + 0 + oo = oo`

So, Answer `= oo`