Evaluate :

`lim_( n -> oo ) ( 1 + 1/2 + 1/4 ---- + 1/2^n ) / ( 1 + 1/3 + 1/9 --- + 1/3^n ) `
1 ) `4/3`
2 ) `3/4`
3 ) `1/2`
4 ) 0

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

lim_ (n rarr oo) (1) / (n) [(1) / (n + 1) + (2) / (n + 2) + ... + (3n) / (4n)]

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

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

lim_ (n rarr oo) [(1 ^ (3)) / (n ^ (4) + 1 ^ (4)) + (2 ^ (3)) / (n ^ (4) + 2 ^ (4)) ++ (1) / (2n)] =

lim_ (n rarr oo) [(1) / (1.2) + (1) / (2.3) + (1) / (3.4) + ... + (1) / (n (n + 1))] =

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

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

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))