Let \(\alpha =\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\ldots \infty\) and \(\beta =\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\ld…

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:

[JEE Main 2026, 4 Apr (Shift 2)]