Evaluate :
`lim_( n -> oo ) 1/n^3 { 1 + 3 + 6 + --- + ( n ( n +1 )) /2 }`
( 1 ) 0
( 2 ) 2
( 3 ) `1/6`
( 4 )` 1/3`

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

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

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

Value of lim_ (n rarr oo) (1 ^ (3) + 2 ^ (3) + 3 ^ (3) ... + n ^ (3)) / (n ^ (4))

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

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))

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

lim_ (n rarr oo) (1.2 + 2.3 + 3.4 + .... + n (n + 1)) / (n ^ (3))