Evaluate the following limit : lim(n→∞) ((n + 2)! + (n + 1)!)/((n + 2)! - (n - 1)!)

Question

Evaluate the following limit : \(\lim\limits_{\text x \to \infty}\cfrac{(n+2)!+(n+1)!}{(n+2)!-(n-1)!} \)

lim(n→∞) ((n + 2)! + (n + 1)!)/((n + 2)! - (n - 1)!)

Answer 1

Given: \(\lim\limits_{\text x \to \infty}\cfrac{(n+2)!+(n+1)!}{(n+2)!-(n-1)!} \)

We know that, (n + 2)! = (n + 2) × (n + 1)!

By putting the value of (n + 2)! , we get

Hence, \(\lim\limits_{\text x \to \infty}\cfrac{(n+2)!+(n+1)!}{(n+2)!-(n-1)!} \) = 1