Show that :
`lim_( n -> oo ) ( 1^2 + 2^2 + 3^2 --- n^2 ) / n^3 = 1/3`

lim_(n->oo) [ (1^3+ 2^3 + 3^3 -------n^3)/n^4]

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

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

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

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

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

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

Evaluate: lim_ (n rarr oo) (1 ^ (4) + 2 ^ (4) + 3 ^ (4) + ... + n ^ (4)) / (n ^ (5)) - lim_ (n rarr oo) (1 ^ (3) + 2 ^ (3) + ... + n ^ (3)) / (n ^ (5))

Evaluate: lim_ (n rarr oo) (1 ^ (4) + 2 ^ (4) + 3 ^ (4) + ... + n ^ (4)) / (n ^ (5)) - lim_ (n rarr oo) (1 ^ (3) + 2 ^ (3) + ... + n ^ (3)) / (n ^ (5))

The value of lim_(x to oo) (1 + 2 + 3 … + n)/(n^(2)) is