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

lim_(n rarr oo)(n^(2))/(2^(n))

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

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

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

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

lim_(n rarr oo)(2^(3n))/(3^(2n))=

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

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

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

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