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): underset(n rarr infty)lim{(1+1/n)(1+2/n)…(1+n/n)}^(1/n)

Evaluate (with the help of definite integral) : underset(n to oo)lim[(1)/(sqrt(n))+(1)/(sqrt(2n))+(1)/(sqrt(3n))+…+(1)/(n)]

Evaluate (with the help of definite integral) underset(nrarr infty) It ((1)/(n+1) + (1)/(n+2) + ….. + (1)/(6n))

Evaluate: lim_(n->oo)(4^n+5^n)^(1/n)

Evaluate (with the help of definite integral) underset(n rarr infty)lim[1/sqrtn+1/sqrt(2n)+1/sqrt(3n)+….+1/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 the following define integrals as limit of sums : lim_(n rarroo) [(1+1/n) (1+2/n)......(1+n/n)]^(1//n)

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