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" Evaluate: "lim(x rarr oo)[(1^(3)+2^(3)...

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

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Evaluate: lim_(x rarr oo)[(1^3+2^3+3^3+...........+x^3)/x^4]

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 ^ (3) + 2 ^ (3) ++ n ^ (3)) / ((n-1) ^ (4))

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

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

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