Evaluate `lim_(n->infty) root(3)(n^2-n^3)+n`

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

The value of lim_(ntooo) [root(3)((n+1)^(2))-root(3)((n-1)^(2))] is __________.

The value of lim_(n rarr infty) (1)/(n) {(n+)(n+2)(n+3)…(n+n)}^(1//n) is equal to

Evaluate: lim_(n rarr oo)((1)/(n^(2)+1)+(2)/(n^(2)+2)+(3)/(n^(2)+3)+...+(n)/(n^(2)+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_(nrarroo) [1/(n+1) + 1/(n+2) + 1/(n+3) +…+ 1/(2n)]