`lm_(n->oo)(1^3/n^4+2^4/n^4+3^3/n^4+........+n^3/n^4)`

Evaluate : lim_(n-> oo) (1^4+2^4+3^4+...+n^4)/n^5 - lim_(n->oo) (1^3+2^3+...+n^3)/n^5

The value of lim_(n rarr oo)(1/(1-n^4)+8/(1-n^4)+...+n^3/(1-n^4)) is

lim_(n->oo) [ (1^3+ 2^3 + 3^3 -------n^3)/n^4]

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 ^ (4) + 3 ^ (4) + ...... + n ^ (4)) / (n ^ (5))) - lim_ (n rarr oo ) ((1 + 2 ^ (6) + 3 ^ (6) + .... + n ^ (6)) / (n ^ (7)))

lim_(n rarr oo) (1.2 +2.3+3.4+ .....+n(n+1))/n^(3)=

lim_(n->oo) (1.2+2.3+3.4+....+n(n+1))/n^3

Evaluate the following limit: (lim)_(n->oo)(1^3+2^3+ n^3)/((n-1)^4)