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

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

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

lim_(n rarr oo)(1+2^(4)+3^(4)+...+n^(4))/(n^(5))

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

The value of lim_(n rarr oo) (1 + 2^(4) + 3^(4) +…...+n^(4))/(n^(5)) - lim_(n rarr oo) (1 + 2^(3) + 3^(3) +…...+n^(3))/(n^(5)) is :

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

lim_ (n rarr oo) (1 + 3 + 6 ++ (1) / (2) n (n + 1)) / (n ^ (3))

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

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

lim_ (n rarr oo) ((n + 2)! + (n + 1)!) / ((n + 3)!)