Sequence And Series Question 55
Question: $ \frac{4}{1,.,3}-\frac{6}{2.4}+\frac{12}{5,.,7}-\frac{14}{6,.,8}+…..\infty = $
Options:
A) $ {\log_{e}}3 $
B) $ {\log_{e}}2 $
C) $ 2,{\log_{e}}2 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ S=\frac{4}{1.3}-\frac{6}{2.4}+\frac{12}{5.7}-\frac{14}{6.8} $ +…. $ =\frac{1+3}{1.3}-\frac{2+4}{2.4}+\frac{5+7}{5.7}-\frac{6+8}{6.8}+…. $ $ =( \frac{1}{1}+\frac{1}{3} )-( \frac{1}{2}+\frac{1}{4} )-( \frac{1}{5}+\frac{1}{7} )-( \frac{1}{6}+\frac{1}{8} )+…. $ $ =1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+….={\log_{e}}2 $ .
BETA
