Sq.rt (n)/ln(n) is a convergent or divergent series where n is from 1 to infinity?

Answer 1

Use the test for divergence:
lim (n->inf) [sqrt(n) / ln(n)]
= (l'hopital's rule) lim (n->inf) [1/(2 sqrt(n)) / (1/n)]
= lim (n->inf) [n / 2 sqrt(n)]
= lim (n->inf) [sqrt(n) / 2]
= inf

The elements in this series continually increases until infinity. The series diverges.

Answer 2

sqrt(n) / ln(n) ==> infinity so the series is divergent
Apply L´Hôpital to lim x^1/2/ln x =lim (1/2 x^1/2)==> infinity