I'm completely clueless on this one. I can easily calculate the limit using L'Hopital's rule, but proving that the series is converging to 0 is far more tricky.
$$a_n= {n \over 2^n}$$
Any help?
Answer
Using the fact that $2^n>n^2$ for $n > 4$, we have: $$0 \leq a_n < \frac{n}{n^2}=\frac{1}{n}.$$
Hence, $\displaystyle \lim_{n \to \infty}a_n=0.$
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