Evaluate :
`underset(n to oo)lim(n)/((n!)^((1)/(n)))`

Evaluate : underset(n to oo) lim[(1)/(n)+(1)/(n+1)+(1)/(n+2)+…+(1)/(4n)]

Evaluate : underset(n to oo) lim[(1)/(n)+(1)/(n+1)+(1)/(n+2)+…+(1)/(3n)]

Evaluate : underset(n to oo) lim[(1+(1)/(n))(1+(2)/(n))(1+(3)/(n))…(1+(n)/(n))]^((1)/(n))

Evaluate : underset(n to oo)lim [((2n)!)/(n!n^(n))]^((1)/(n))

The value of underset(n to oo)lim((n!)^((1)/(n)))/(n) is -

underset(n to oo)lim (2^(n)-n)/(2^(n))=

underset(n to oo)lim (2^(n)-1)/(3^(n)+1)=

underset(n to oo)lim (5^(n)+1)/(3^(n)-1)=

Evaluate : underset(n to oo) lim[((1+1^(2)/n^(2)))(1+(2^(2))/(n^(2)))(1+(3^(2))/(n^(2)))…(1+(n^(2))/(n^(2)))]^((1)/(n))

underset(n to oo)lim""((n!)^(1//n))/(n) equals :