Logarithm

Let $\alpha=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\ldots \infty$ and


$\beta=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\ldots \infty$. Then the value of


$(0.2)^{\log _{\sqrt{5}}(\alpha)}+(0.04)^{\log _5(\beta)}$ is equal to :