Evaluate(with the help of definite integral): `lim_(n->oo) {(1+1/n)(1+2/n)...(1+n/n)}^[1/n]`

Evaluate(with the help of definite integral): lim_(n rarr oo){(1+(1)/(n))(1+(2)/(n))dots(1+(n)/(n))}^((1)/(n))

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

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

lim_(n rarr oo)((-1)^(n)n)/(n+1)

Find the value of lim_(n rarr oo)(1)/(n)+(1)/(n+1)+(1)/(n+2)+...+(1)/(4n)

Evaluate the following (i) lim_(n to oo)((1)/(n^(2))+(2)/(n^(2))+(3)/(n^(2))....+(n-1)/(n^(2))) (ii) lim_(n to oo)((1)/(n+1)+(1)/(n+2)+....+(1)/(2n)) (iii) lim_(n to oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+....+(n)/(2n^(2))) (iv) lim_(n to oo)((1^(p)+2^(p)+.....+n^(p)))/(n^(p+1)),pgt0

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

Find lim_ (n rarr oo) n ^ (n) (1 + n) ^ (- n)

Evaluate: (lim)_(n rarr oo)[(n!)/(n^(n))]^(1/n)