If ∑n=0∞arn=S\displaystyle \sum_{n=0}^{\infty} ar^n = Sn=0∑∞arn=S where ∣r∣<1|r| < 1∣r∣<1, what is ∑n=0∞a2r2n\displaystyle \sum_{n=0}^{\infty} a^2 r^{2n}n=0∑∞a2r2n in terms of SSS?
S2S^2S2
S2(1−r)1+r\displaystyle \frac{S^2(1-r)}{1+r}1+rS2(1−r)
a21−r2\displaystyle \frac{a^2}{1-r^2}1−r2a2
S(1−r2)S(1-r^2)S(1−r2)