# Recent content by RKermanshahi

1. ### Lim of P(n)/(a^n) = 0

Thanks, Dick. I actually solved it using the monotone convergence theorem. I took the quotient xn/xn+1 and showed that it was eventually always less than one (and hence eventually decreasing). I then showed it was bounded. So by the monotone convergence theorem it converges. Finally, taking...
2. ### Lim of P(n)/(a^n) = 0

So taking the log's of both sides and applying rules of log's we get: log(x_n)/n= (alogn)/n + logb. Is there a way to show (a logn)/n goes to zero as n goes to infinity without using L'Hospital's rule?
3. ### Lim of P(n)/(a^n) = 0

1. Consider the sequence xn=nabn, where a is a natural number and b is a real number with 0<b<1. Show that the sequence converges to zero. Conclude from here that lim P(n)/cn=0, where P is a polynomial function and c>1. 2. I am not sure how to show that the sequence converges to zero...