Question

The sum of series $1,\frac{1}{3},\frac{1}{9},\frac{1}{27},\frac{1}{81}.....$ is ___.

• A. $\frac{3}{2}$
• B. $\frac{4}{7}$
• C. $\frac{9}{5}$
• D. $\frac{3}{8}$

Answer 1

The correct option is A

$\frac{3}{2}$

The sum of an infinite GP whose first term $a$ and common ratio $r$, where -1 < r < 1 (i.e., |r| < 1) is

$S=\frac{a}{1-r}.$

Here, $a=1$ and $r=\frac{t_2}{t_1}=\frac{\frac{1}{3}}{1}=\frac{1}{3}.$

Hence, we get $S=\frac{a}{1-r}=\frac{1}{1-\frac{1}{3}}=\frac{1}{\frac{2}{3}}=\frac{3}{2}.$