Question

The value of $\left(0.2\right)^{\log_{\sqrt{5}}\left(\frac{1}{4} + \frac{1}{8} + \frac{1}{6} + .... to \, \infty\right)}$

• A. 4
• B. 44565
• C. 2
• D. 44563

Answer 1

Answer: (A)

4

Answer 2

$0.2^{\log_{\sqrt{5}}\left(\frac{1}{4} + \frac{1}{8} + \frac{1}{6} + .... to \infty\right)}$
$= \left(\frac{1}{5}\right)^{\log _{\sqrt{5}} \left(\frac{1}{2}\right)} = \left(\frac{1}{5}\right)^{2 \log _{\sqrt{5}}}\left(\frac{1}{2}\right)$
$= \left(5\right)^{-2\log _{5}} \left(\frac{1}{2}\right) = \left(5\right)^{\log _{5}4} = 4$