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If $f(x+y) = f(x)f(y)$ and $\sum_{x=1}^{\infty} f(x) = 2$, $x, y \in \mathbb{N}$, then the value of $\frac{f(4)}{f(2)}$ is:
(1) $\frac{2}{3}$
(2) $\frac{1}{9}$
(3) $\frac{1}{3}$
(4) $\frac{4}{9}$
Type: MCQ
$\frac{k}{1-k} = 2 \Rightarrow k = \frac{2}{3}$
$\frac{f(4)}{f(2)} = k^2 = \frac{4}{9}$
BETA
