Question

The value of $(0.2{)}^{{\log }_{\sqrt{5}}\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\dots \infty \right)}$ is equal to

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

Answer: (B)

$=0.2{\log }_{\sqrt{5}}\left[\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\dots \dots \dots ..\infty \right]={}_{0.2}{\log }_{\sqrt{5}}\left[\frac{1/4}{1-1/2}\right]={}_{(0.2)}{\log }_{\sqrt{5}}\left[\frac{1}{2}\right]={}_5{\log }_{\sqrt{5}}2=2^2=4$