Question

If the sum of the series $1+\frac{2}{x}$+$\frac{4}{x^2}$+$\frac{8}{x^3}$+...to $\infty$ is the finite number then

• A. $x<2$
• B. $x>\frac{1}{2}$
• C. $x>-2$
• D. $x<-2$ or $x>2$

Answer 1

Answer: (D)

$x<-2$ or $x>2$

Given infinite series is $1+\frac{2}{x}$+$\frac{4}{x^2}$+$\frac{8}{x^3}$+...to $\infty$

As sum to infinity is finite, common ratio $|r|<1$

$\Rightarrow |\frac{2}{x}|<1$

$\Rightarrow |x|>2$

$\therefore x<-2$ or $x>2$