Sequence And Series Question 559
Question: $ 1+\frac{2}{3}-\frac{2}{4}+\frac{2}{5}-……\infty = $
Options:
A) $ {\log_{e}}3 $
B) $ {\log_{e}}4 $
C) $ {\log_{e}}( \frac{e}{2} ) $
D) $ {\log_{e}}( \frac{2}{3} ) $
Show Answer
Answer:
Correct Answer: B
Solution:
$ S=1+2{ \frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+…. } $ $ =( 2-\frac{2}{2} )+2{ \frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+…. } $ $ =2{ 1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+… }=2{\log_{e}}2 $ = $ {\log_{e}}4 $ .
BETA
