Question

The first term of an infinite G.P is $1$ and any term is equal to the sum of all the succeeding terms Find the series

• A. $1,2,4,8,....................$
• B. $1,\frac{1}{3},\frac{1}{9},\frac{1}{27},.................$
• C. $1,\frac{1}{4},\frac{1}{8},....$
• D. $1,\frac{1}{2},\frac{1}{4},\frac{1}{8},....$

Answer 1

The correct option is D $1,\frac{1}{2},\frac{1}{4},\frac{1}{8},....$

Let the G.P is $1,r,r^2,r^3,..........$
Then according to the condition $r=\frac{r^2}{1-r}=\frac{1}{2}$
Hence the series is$1,\frac{1}{2},\frac{1}{4},\frac{1}{8}......$