Sequence And Series Question 70
Question: The sum of the series $ {\log_4}2-{\log_8}2+{\log_{16}}2…. $ is
[MNR 1994; Roorkee 1994; MP PET 2000]
Options:
A) $ e^{2} $
B) $ {\log_{e}}2 $
C) $ {\log_{e}}3-2 $
D) $ 1-{\log_{e}}2 $
Show Answer
Answer:
Correct Answer: D
Solution:
Since $ {\log_{y^{n}}}x^{m}=\frac{m}{n}{\log_{y}}x $ and $ {\log_{x}}x=1 $ .
$ \therefore ,S=\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+…. $ Also $ {\log_{e}}(1+x)=x-\frac{x^{2}}{2}+\frac{x^{3}}{3}-\frac{x^{4}}{4}+…. $ Putting $ x=1,S=1-{\log_{e}}2 $ .
BETA
