The value of _ n (n+2)! + (n+1)! (n+2)! - (n+1)! is ____

Step-by-step solution

The given limit is _ n (n+2)! + (n+1)! (n+2)! - (n+1)! Taking (n+1)! common from both numerator and denominator: _ n (n+1)![(n+2) + 1] (n+1)![(n+2) - 1] Cancelling (n+1)! from numerator and denominator: _ n n+3 n+1 Dividing numerator and denominator by n : _ n 1 + 3 n 1 + 1 n As n , 1 n 0 . Substituting the limit: 1 + 0 1 + 0 = 1 Answer: 1