Find if the subsquent convergent or divergent

Question

1. an= ln(n)/n

 

My answer 

Lim n→∞.  Ln(n)/n

Lim x→∞.  Ln(x)/x

Using L'hospital

Lim x→∞.  1/x

=0 (convergent)

is it correct?

 

2. an+1 = 1 +1/2 an, a1=1

I have no idea how to solve this one

Answer 1

Your title should have the misspelled word 'subsquent' replaced by "sequence" 

 

your #1 answer is correct.

 

write out various a_i values and you will see obvious convergence of a_n+1 toward 2.