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} $
• E. $ \frac{9}{2} $

Answer 1

Answer: (D)

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} $