Sequence And Series Question 64
Question: If $ 4,[ x^{2}+\frac{x^{6}}{3}+\frac{x^{10}}{5}+….. ]=y^{2}+\frac{y^{4}}{2}+\frac{y^{6}}{3}+……, $ then
Options:
A) $ x^{2}y=2x-y $
B) $ x^{2}y=2x+y $
C) $ x=2y^{2}-1 $
D) $ x^{2}y=2x+y^{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
Given equation is, $ 4[ x^{2}+\frac{x^{6}}{3}+\frac{x^{10}}{5}+… ]=y^{2}+\frac{y^{4}}{2}+\frac{y^{6}}{3}+…. $
$ \Rightarrow ,\frac{4}{2}{\log_{e}}( \frac{1+x^{2}}{1-x^{2}} )=-{\log_{e}}(1-y^{2}) $
$ \Rightarrow ,{\log_{e}},{{( \frac{1+x^{2}}{1-x^{2}} )}^{2}}={\log_{e}}( \frac{1}{1-y^{2}} ) $ ;
$ \Rightarrow {{( \frac{1+x^{2}}{1-x^{2}} )}^{2}}=\frac{1}{1-y^{2}} $ On simplification, we get $ x^{2}y=2x-y $ .
BETA
