Let α=1/4+1/8+1/16+… ∞ and β=1/3+1/9+1/27+… ∞. Then the value of (0.2)^log_√ 5 (α) +(0.04)^log_5(β) is equal to:

Let $\displaystyle \alpha=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\ldots \infty$ and $\displaystyle \beta=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\ldots \infty$. Then the value of $\displaystyle (0.2)^{\log _{\sqrt{5}}(\alpha)}+(0.04)^{\log _5(\beta)}$ is equal to: