# NIELIT 2019 Feb Scientist D - Section D: 28

82 views

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

1. $1$
2. $0$
3. $\frac{8}{1-x^{8}}$
4. $\frac{16}{1-x^{16}}$

recategorized

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

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

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

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

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

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

Option $D$ is correct here.
3.5k points 4 10 63

## Related questions

1
87 views
Find all the polynomials with real coefficients $P\left(x \right)$ such that $P\left(x^{2}+x+1 \right)$ divides $P\left(x^{3}-1 \right)$. $ax^{n}$ $ax^{n+2}$ $ax$ $2ax$
2
74 views
The roots of the equation $x^{2/3}+x^{1/3}-2=0$ are : $1, -8$ $-1, -2$ $\frac{2}{3}, \frac{1}{3}$ $-2, -7$
1 vote
If $x^{a}=y^{b}=z^{c}$ and $y^{2}=zx$ then the value of $\frac{1}{a} + \frac{1}{c}$ is : $\frac{b}{2}$ $\frac{c}{2}$ $\frac{2}{b}$ $\frac{2}{a}$
If $t^{2}-4t+1=0$, then the value of $\left[t^{3}+1/t^{3} \right]$ is : $44$ $48$ $52$ $64$
If $a^{x}=b$, $b^{y}=c$ and $c^{z}=a$, then the value of $xyz$ is : $0$ $1$ $\frac{1}{3}$ $\frac{1}{2}$