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

The value of lim_(n rarr oo)(1^(2)*n+2^(2)*(n-1)+......+n^(2)*1)/(1^(3)+2^(3)+......+n^(3)) is equal to

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

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

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

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

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

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

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

lim_(n rarr oo)[(1^(2))/(n^(3))+(2^(2))/(n^(3))+(3^(2))/(n^(3))+...+(n^(2))/(n^(3))]=?