Evaluate :

`lim_( n -> oo ) (( n + 1 )! - n! )/( 5 ( n + 1 )! )`

lim_ (n rarr oo) ((n + 2)! + (n + 1)!) / ((n + 3)!)

Evaluate, lim_ (n rarr oo) ((1 + 4 ^ ((1) / (n))) / (2)) ^ (n)

Using Sandwich theorem, evaluate lim_ (n rarr oo) ((1) / (1 + n ^ (2)) + (1) / (2 + n ^ (2)) + ...... + (n) / (n + n ^ (2)))

lim_(n rarr oo)(n!)/((n+1)!-n!)

Evaluate: lim_ (n rarr oo) (1 ^ (4) + 2 ^ (4) + 3 ^ (4) + ... + n ^ (4)) / (n ^ (5)) - lim_ (n rarr oo) (1 ^ (3) + 2 ^ (3) + ... + n ^ (3)) / (n ^ (5))

Evaluate: lim_ (n rarr oo) (1 ^ (4) + 2 ^ (4) + 3 ^ (4) + ... + n ^ (4)) / (n ^ (5)) - lim_ (n rarr oo) (1 ^ (3) + 2 ^ (3) + ... + n ^ (3)) / (n ^ (5))

evaluate lim_ (n rarr oo) ((e ^ (n)) / (pi)) ^ ((1) / (n))

Evaluate: lim_ (n rarr oo) (1 * 2 + 2 * 3 + 3 * 4 + ... + n (n + 1)) / (n ^ (3))

lim_ (n rarr oo) (2 ^ (n) -1) / (2 ^ (n) +1)