Question

If $S=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+....\infty$.
then, the sum of the given series is $2$.

• A. True
• B. False

Answer 1

The correct option is A True

We have,

$S=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+....\infty$

Then,

$a=1$, $r=\frac{1}{2}$

We know that

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

$S=\frac{1}{1-\frac{1}{2}}$

$S=\frac{1}{\frac{1}{2}}$

$S=2$

Hence, this is the answer.