Question

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

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

Answer 1

The correct option is A $x>2$

The series $1+\frac{2}{x}+....$ forms GP

with $a=1r=\frac{2}{x}$

The sum becomes finte only if $r<1\frac{2}{x}<1x>2$