حل فرع الاول
suppose that an =(3n) ^ 1/2n take ln both sides
ln(an)= ln(2n)/ 3n
as n go to infinity
the rhigt side use lopital rule
we get 0 as n go to infinity
ln(an) go to 0 as n go to infinity
an go to to e^ 0 = 1
SO lim (3n) ^ 1/2n = 1
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