# The sum $1+\frac{3}{x}+\frac{9}{x^2}+\frac{27}{x^3}+....\infty$, ($x\neq\;0$) is finite if

$(a)\;|x| < 1\qquad(b)\;|x| > 1 \qquad(c)\;|x| < 3\qquad(d)\;|x| >3$

Answer : (d) $|x| > 3$
Explanation : For sum of an infinite series to be finite , common difference should be less than 1 .
$|\frac{3}{x} |< 1$
$|x| > 3\;.$