Answer
Divergent
Work Step by Step
The sum of a geometric series can be found as:
$S=\dfrac{a}{1-r}$
The given series $\sum_{n=0}^{\infty} (\sqrt 2)^n$ has the first term, $a=1$, and a common ratio $r =\sqrt 2 \gt 1$
Hence, the given series $\sum_{n=0}^{\infty} (\sqrt 2)^n$ is divergent.
