The sequence $a_k$ = $3/2\sum_{k=1}^{\infty}\frac{1}{4^k}$
Does the series converge? Compute $\liminf a_k^{1/k}$, $\limsup a_k^{1/k}$, $\liminf a_{k+1}/a_k$ and $\limsup a_{k+1}/a_k$ as $k\to\infty$
How do we show this? Thank you!
I think by ratio test, this is convergent. And $a_{k+1}/a_k$ = 1/4 and then?