Question

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

• A. Cannot be determined.
• B. Equals $\frac{15}{8}$
• C. Equals $2$
• D. Will be higher than $2$.

Answer 1

The correct option is C Equals $2$

$GivenseriesisaninfiniteGPwithfirstterm=1andcommonratio=1/2\therefore sum=\left(\frac{a}{1-r}\right)=\left(\frac{a}{1-1/2}\right)=2$