Question

The first term of an infinite $GP$ is $1$ and each term is twice the sum of the succeeding terms, then the sum of the series is

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

Answer 1

Answer: (D)

$\frac{3}{2}$

Answer 2

According to question $1=2(r+{{r}^{2}}+{{r}^{3}}+....)$ $\frac{1}{2}=\frac{r}{1-r}$
$\Rightarrow$ $r=\frac{1}{3}$
$\therefore$ The series is $1,\frac{1}{3},\frac{1}{9},\frac{1}{27},......$ Required sum
$=1+\frac{1}{3}+\frac{1}{9}+.....$
$=\frac{1}{1-\frac{1}{3}}=\frac{3}{2}$