(a) As n \to \infty implies x^n \to 0 and x^{n+1} \to 0 since both of absolute value less than 1. So f(x) \to 1
(b) S_O=\frac{F_{2k}}{F_{2k-1}}=\frac{F_{2k-1}}{F_{2k-1}}+\frac{F_{2k-2}}{F_{2k-1}}=1+\frac{F_{2k-2}}{F_{2k-1}} where k is a positive integer. But since the fibonacci sequence is...