Evaluate: `("lim")_(nvecoo)((1^2+2^2+3^3++n^2)(1^3+2^3+3^3++n^3))/(1^6+2^6+3^6++n^6)`

Evaluate lim_(nrarroo) [(1^6 + 2^6 + 3^6…..+n^6)/n^7]

Evaluate lim _( x to oo) ((1^(2) )/(n ^(3) +1 ^(3))+(2 ^(2))/(n ^(3) +2 ^(3)) + (3 ^(2))/(n ^(3)+ 3 ^(3))+ .... + (4)/(9n)).

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

lim_(n to oo) [ 1^2/n^3 + (2^2)/(n^3) + …+ ((n-1)^2)/(n^3)]

Evaluate lim_(ntooo) (1^(3)+2^(3)+3^(3)+...+n^(3))/(sqrt(4n^(8)+1)).

Evaluate: lim_ (n rarr oo) (1 * 2 + 2 * 3 + 3 * 4 + ... + n (n + 1)) / (n ^ (3))

"Evaluate "Sigma_(n=1)^(6) (3+2^(n)).

lim_ (n rarr oo) (1 + 3 + 6 ++ (1) / (2) n (n + 1)) / (n ^ (3))

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