Answer
Converges
Work Step by Step
The sum of a geometric series can be found as:
$S_n=\dfrac{a_1}{1-r}$
where, $a_1$ denotes the first term and the $r$ is common ratio.
We are given that $\Sigma_{n=0}^{\infty} (0.36)^n$
This can be further written as: $\Sigma_{n=0}^{\infty} (0.36)^n=0.36+(0.36)^2+(0.36)^3+.......$
So, we have $a_1=0.36$ and $r=0.36$
Thus, we can see that $|r|=0.36 \lt 1$. This means that the given series converges.
