$a_n=1$ if $n=2^k$ for $k>0$
$a_n=\frac{1}{n!}$ otherwise
a) Find limsup $\displaystyle \frac{|a_{n+1}|}{|a_n|}$ - I think this is infinity because we can find a term that is 1/something!, but the next term will be 1, so the ratio will be something! which can be made infinitely large.
b) limsup $\displaystyle |a_n|^{\frac{1}{n}}$ - I think this is 1 because the maximum we can have is 1^1, rather than a fraction^1.
Am I correct?
