Sequence And Series Question 42
Question: $ \frac{1}{5}+\frac{1}{2},.,\frac{1}{5^{2}}+\frac{1}{3}.\frac{1}{5^{3}}+…..\infty = $
Options:
A) $ {\log_{e}}\frac{4}{5} $
B) $ {\log_{e}}\frac{\sqrt{5}}{2} $
C) $ 2{\log_{e}}\frac{\sqrt{5}}{2} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{1}{5}+\frac{1}{2}.\frac{1}{5^{2}}+\frac{1}{3}.\frac{1}{5^{3}}+….. $ $ =-{\log_{e}}( 1-\frac{1}{5} )={\log_{e}}( \frac{5}{4} )={\log_{e}}{{( \frac{\sqrt{5}}{2} )}^{2}}=2{\log_{e}}( \frac{\sqrt{5}}{2} ) $ .
BETA
