sequences?

Question

Determine the convergence or divergence of the sequence with the n th term equal to a(sub n) = lnsqrt(n) / n. If it converges find it's limit.

Answer 1

I'll use the basic and well known fact that lim ln(n)/n = 0. And also, ln(sqrt(n) = 1/2 ln(n)

For every n, ln(sqrt(n)/n = 1/2 ln(n) /n. So, lim ln(sqrt(n)/n =1/2 lim ln(n)/n = 1/2 * 0 = 0