First slide

Geometric progression

Question

The value of 0.2 $^{\log_{\sqrt{5}} (\frac{1}{4} + \frac{1}{8} + \frac{1}{16} + ......)} is$

Moderate

A

4
B

log 4
C

log 2
D

log 3

Solution

$We have, \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \dots = \frac{1 / 4}{1 - 1 / 2} = \frac{1}{2}$
$\begin{aligned} {0.2}^{\log \sqrt{5} (\frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \dots .)} = 0 . 2^{\log_{\sqrt{5}} (\frac{1}{2})} \\ = {(\frac{1}{5})}^{^{\log_{\sqrt{5}} (\frac{1}{2})}} \end{aligned}$
$\begin{aligned} = {(5^{- 1})}^{2 \log_{5} (\frac{1}{2})} \\ = (5)^{- 2 \log_{5} (\frac{1}{2})} \\ = (5)^{\log_{5} 4} = 4 \end{aligned}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App