Sequence And Series Question 350
$ {{( x+\frac{1}{x} )}^{2}}+{{( x^{2}+\frac{1}{x^{2}} )}^{2}}+{{( x+\frac{1}{x^{3}} )}^{2}}…. $ upto n terms is
Options:
A) $ \frac{x^{2n}-1}{x^{2}-1}\times \frac{{x^{2n+2}}+1}{x^{2n}}+2n $
B) $ \frac{x^{2n}+1}{x^{2}+1}\times \frac{{x^{2n+2}}-1}{x^{2n}}-2n $
C) $ \frac{x^{2n}-1}{x^{2}-1}\times \frac{x^{2n}-1}{x^{2n}}-2n $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
[a] The series is $ (x^{2}+x^{4}+x^{6}+\text{up to }n\text{ terms}) $ $ +\left( \frac{1}{x^{2}}+\frac{1}{x^{4}}+\frac{1}{x^{6}}+\text{up to }n\text{ terms} \right)\text{+2+up to }n\text{ terms)} $ $ a=\frac{x^{2}(x^{2n}-1)}{x^{2}-1}+\frac{\frac{1}{x^{2}}( 1-\frac{1}{x^{2n}} )}{1-\frac{1}{x^{2}}}+2n $ $ =\frac{x^{2}(x^{2n}-1)}{x^{2}-1}+\frac{x^{2n}-1}{(x^{2}-1)x^{2n}}+2n $ $ =,\frac{x^{2n}-1}{x^{2}-1}\times \frac{{x^{2n+2}}+1}{x^{2n}}+2n $
BETA
