What is the sum of the series ∑n=0∞r2n\sum_{n=0}^{\infty} r^{2^n}∑n=0∞r2n for ∣r∣<1|r|<1∣r∣<1?
r1−r\frac{r}{1-r}1−rr
Does not have a closed form
11−r\frac{1}{1-r}1−r1
r21−r2\frac{r^2}{1-r^2}1−r2r2