Lakshman Bhaiya
asked
in Quantitative Aptitude
Apr 3, 2020
recategorized
Nov 8, 2020
by Krithiga2101

574 views
1 vote

$\left [ \frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}\right ]$

$\implies \left [ \frac{2}{1-x^2}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}\right ]$

$\implies \left [ \frac{4}{1-x^4}+\frac{4}{1+x^4}+\frac{8}{1+x^8}\right ]$

$\implies \left [ \frac{8}{1-x^8}+\frac{8}{1+x^8}\right ]$

$\implies \left [ \frac{16}{1-x^{16}}\right ]$

Note: take the first 2 term's in each steps and solve them using LCM.

Option $D$ is correct here.

$\implies \left [ \frac{2}{1-x^2}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}\right ]$

$\implies \left [ \frac{4}{1-x^4}+\frac{4}{1+x^4}+\frac{8}{1+x^8}\right ]$

$\implies \left [ \frac{8}{1-x^8}+\frac{8}{1+x^8}\right ]$

$\implies \left [ \frac{16}{1-x^{16}}\right ]$

Note: take the first 2 term's in each steps and solve them using LCM.

Option $D$ is correct here.