Sequence And Series Question 44
In the expansion of $ 2{\log_{e}}x-{\log_{e}}(x+1)-{\log_{e}}(x-1) $ , the coefficient of $ {x^{-4}} $ is
Options:
1/2
B) $ -1 $
1
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ 2{\log_{e}}x-{\log_{e}}{ ( 1+\frac{1}{x} )x }-{\log_{e}}{ ( 1-\frac{1}{x} )x } $ $ =2{\log_{e}}x-{ {\log_{e}}( 1+\frac{1}{x} )+{\log_{e}}x } $ $ -{ {\log_{e}}( 1-\frac{1}{x} )+{\log_{e}}x } $ $ =-{ {\log_{e}}( 1+\frac{1}{x} )+{\log_{e}}( 1-\frac{1}{x} ) }=2{ \frac{1}{2x^{2}}+\frac{1}{4x^{4}}+……. } $ The coefficient of $ {x^{-4}}=2.\frac{1}{4}=\frac{1}{2} $ .
BETA
