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

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

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)(2^(3n))/(3^(2n))=

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

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

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+2+3+...+n)

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

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