Question

Find the sum of the infinite geometric series $1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+.......$

• A. $16$
• B. $14$
• C. $-11$
• D. $2$

Answer 1

The correct option is D $2$

Given sequence is $1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....$

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

Therefore, $\text{sum}=\frac{a}{1-r}$

$\Rightarrow \text{sum}=\frac{1}{1-\frac{1}{2}}$

$\Rightarrow \text{sum}=2$