Sequence And Series Question 48
Question: The sum of the series $ \frac{1}{2,.,3}+\frac{1}{4,.,5}+\frac{1}{6,.,7}+…= $
[MP PET 1998]
Options:
A) $ \log ,(2/e) $
B) $ \log ,(e/2) $
C) 2/e
D) e/2
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{1}{2.3}+\frac{1}{4.5}+\frac{1}{6.7}+….. $ $ =( \frac{1}{2}-\frac{1}{3} )+( \frac{1}{4}-\frac{1}{5} )+( \frac{1}{6}-\frac{1}{7} )+……\infty =1-{\log_{e}}2 $ $ ={\log_{e}}e-{\log_{e}}2=\log ( \frac{e}{2} ) $ .
BETA
