## University Calculus: Early Transcendentals (3rd Edition)

$2+\sqrt 2$
The sum of a geometric series can be found as: $S=\dfrac{a}{1-r}$ Here, $a=1, r=\dfrac{1}{\sqrt 2} \lt 1$ Thus, $S=\dfrac{a}{1-r}=\dfrac{1}{1-\dfrac{1}{\sqrt 2}}=\dfrac{\sqrt 2}{\sqrt 2-1}=2+\sqrt 2$