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

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

lim_(n to oo) [ 1/(n^2) + 2/(n^2) + … + n/(n^2)]

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

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

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

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

Evaluate lim_(n rarr oo)n[(1)/((n+1)(n+2))+(1)/((n+2)(n+4))++(1)/(6n^(2))]

lim_(n rarr oo) (1^2/(1-n^3)+2^2/(1-n^3)+...+n^2/(1-n^3))=

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

Evaluate lim_(nto oo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!)