Evaluate :
`lim_( n -> oo ) ( 1 + 1/2 + 1/4 --- 1/2^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))

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

Evaluate lim_ (n rarr oo) [(1+ (1) / (n)) 91+ (2) / (n)) .... (1+ (n) / (n))] ^ ((1) /(a))

Evaluate, lim_ (n rarr oo) ((1 + 4 ^ ((1) / (n))) / (2)) ^ (n)

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

Evaluate lim_ (n rarr oo) (1) / (n) sum_ (r = n + 1) ^ (2n) log_ (e) (1+ (r) / (n))

Using Sandwich theorem, evaluate lim_ (n rarr oo) ((1) / (1 + n ^ (2)) + (1) / (2 + n ^ (2)) + ...... + (n) / (n + n ^ (2)))

Evalute lim_ (n rarr oo) [(1) / ((n + 1) (n + 2)) + (1) / ((n + 2) (n + 4)) + ...... + ( 1) / (6n ^ (2))]