Answer
Diverges
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 $\Sigma_{n=0}^{\infty} (1.67)^n$
This can be further written as: $\Sigma_{n=0}^{\infty} (1.67)^n=1.67+(1.67)^2+(1.67)^3+.......$
So, we have $a_1=1.67$ and $r=1.67$
Thus, we can see that $|r|=1.67 \gt 1$. This means that the given series diverges.
