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

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

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

The value of [lim_(n to oo)(1+2^(4)+3^(4)+...+n^(4))/(n^(5))-lim_(n to oo)(1+2^(3)+3^(3)+...+n^(3))/(n^(5))] is equal to -

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

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

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