Answer
$2+\sqrt 2$
Work Step by Step
Formula to calculate the sum of a geometric series is
$S=\dfrac{a}{1-r}$
with $a=1, r=\dfrac{1}{\sqrt 2} \lt 1$
Now,
$S=\dfrac{a}{1-r}=\dfrac{1}{1-[\dfrac{1}{\sqrt 2}]}$
or, $=\dfrac{\sqrt 2}{\sqrt 2-1}$
or, $=2+\sqrt 2$
