The value of `lim_(n->oo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!)` is a. 1 b . -1 c. 0 d. none of these

Explanation

To solve the limit \( \lim_{n \to \infty} \frac{(n+2)! + (n+1)!}{(n+2)! - (n+1)!} \), we can follow these steps:

### Step 1: Factor out the common terms
In both the numerator and the denominator, we can factor out \((n+2)!\).

The expression becomes:
\[
\lim_{n \to \infty} \frac{(n+2)! \left(1 + \frac{(n+1)!}{(n+2)!}\right)}{(n+2)! \left(1 - \frac{(n+1)!}{(n+2)!}\right)}
...