Evaluate :
`lim_( n -> oo ) logn/n `

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

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

The value of lim_(n rarr oo) n[log(n+1)-logn] is

Evaluate: lim_(n rarr oo)(((n+1)(n+2)...(n+n))^((1)/(n)))/(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_(x rarr oo)sin^(n)((2 pi n)/(3n+1)),n in N

Evaluate lim_ (n rarr oo) [(1+ (1) / (n)) 91+ (2) / (n)) .... (1+ (n) / (n))] ^ ((1) /(a))

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