Evaluate :

`lim_( n -> oo ) e^(-n )`

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

Evaluate lim_ (n rarr oo) (1) / (n) sum_ (r = n + 1) ^ (2n) log_ (e) (1+ (r) / (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)(n^(p)sin^(2)(n!))/(n+1)

Evaluate: lim_(n rarr oo)(4^(n)+5^(n))^((1)/(n))

Evaluate :lim_(n rarr oo)sum_(r=1)^(n)(1)/((n^(2)+r^(2))^(1/2))

Evaluate: (lim)_(n rarr oo)[(n!)/(n^(n))]^(1/n)

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