`lim_(n rarr oo) (1 + 1/2 + 1/4 + . . . + 1/2^n)`

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

lim_ (n rarr oo) (1 * 1! + 2 * 2! + ...... n * n!) / ((n + 1)!)

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

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

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

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

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

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