Answer
First five terms are: $0.78539816; 0.61685028; 0.48447307; 0.38050426; 0.29884735$
We see that $\lim\limits_{n \to \infty} \dfrac{\pi^n}{4^n}=\lim\limits_{n \to \infty} (\dfrac{\pi}{4})^n=0$
Therefore, the given series converges to $0$.
Work Step by Step
Plugging $n = {1,2,3,4,5}$ in $\dfrac{\pi^n}{4^n}$.
$\implies n=1$: $\dfrac{\pi^1}{4^1}=0.78539816$
$\implies n=2$: $\dfrac{\pi^2}{4^2}=0.61685028$
$\implies n=3$: $\dfrac{\pi^3}{4^3}=0.48447307$
$\implies n=4$: $\dfrac{\pi^4}{4^4}=0.38050426$
$\implies n=5$: $\dfrac{\pi^5}{4^5}=0.29884735$
We see that $\lim\limits_{n \to \infty} \dfrac{\pi^n}{4^n}=\lim\limits_{n \to \infty} (\dfrac{\pi}{4})^n=0$
Therefore, the given series converges to $0$.
