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

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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

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

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

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lim(n->oo)(1^2+2^2+3^2+..........+n^2)/n^3

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

The value of lim_(nto oo)(1^(3)+2^(3)+3^(3)+……..+n^(3))/((n^(2)+1)^(2))

Find a for which lim_(n->oo) (1^a+2^a+3^a+...+n^a)/((n+1)^(a-1)[(na+1)+(na+2)+...+(na+n)])=1/60