Sequence And Series Question 39
Question: $ ( \frac{a-b}{a} )+\frac{1}{2}{{( \frac{a-b}{a} )}^{2}}+\frac{1}{3},{{( \frac{a-b}{a} )}^{3}}+…..= $
[MNR 1979; MP PET 1990; UPSEAT 2001, 02; AMU 2005]
Options:
A) $ {\log_{e}}(a-b) $
B) $ {\log_{e}}( \frac{a}{b} ) $
C) $ {\log_{e}}( \frac{b}{a} ) $
D) $ {e^{( \frac{a-b}{a} )}} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ ( \frac{a-b}{a} )+\frac{1}{2}{{( \frac{a-b}{a} )}^{2}}+\frac{1}{3}{{( \frac{a-b}{a} )}^{3}}+…… $ $ =-{\log_{e}}( 1-\frac{a-b}{a} )=-{\log_{e}}( \frac{b}{a} )={\log_{e}}( \frac{a}{b} ) $ .
BETA
