Hi
Could you rewrite with parentheses so that we can understand which are the numerator and the denominator ?
for denominator as n gets larger (0.5)^n will converge to 0 so limit will be 2
but 2n-9 will increase as n gets larger not sure what happen guess it will not be convergent.
i am guessing the sequence will behave like-9/2 mulitiply by 2n which is not convergent ?