Evaluate: `lim_(nrarr0) (((2n)!)/(n!n^(n)))^(1/n)`

lim_(n rarr0)((1+cos n)/(n^(2)))

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

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

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

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

Evaluate: lim_(n rarr oo)n^(-n^(2)){(n+2^(0))n+2^(-1))(n+2^(-2))(n+2^(-n+1))}^(n)

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

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

Evaluate: lim_(n to infty) (n!)/((n+1)!-n!)

Evaluate lim_(ntooo) n^(-n^(2))[(n+2^(0))(n+2^(-1))(n+2^(-2))...(n+2^(-n+1))]^(n) .