Answer
Divergent
Work Step by Step
Formula to calculate the sum of a geometric series is:$S=\dfrac{a}{1-r}$
Here, the series $\sum_{n=0}^{\infty} (\sqrt 2)^n$ has initial term, $a=1$
with common ratio $r =\sqrt 2 \gt 1$
Hence, the series $\sum_{n=0}^{\infty} (\sqrt 2)^n$ is divergent.
