Evaluate :

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

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

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

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

Evaluate lim _( n to oo) sum_( r =1) ^(n -1) (1)/(sqrt(n ^(2) -r ^(2)))

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

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

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