Question

Solve this
The sum of n terms of the series 1+1/2+1/2^2+1/2^3+....​

Answer 1

Answer:

The answer is  $2-\dfrac{1}{2^{n-1}}$

Step-by-step explanation:

Given sum is

 $1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...$n terms

Clearly above series is geometric with first term 1 and common ratio $\dfrac{1}{2}$

Therefore

         $\text{S}_n=\dfrac{a(1-r^n)}{1-r}=\dfrac{1(1-(\frac{1}{2})^n}{1-\frac{1}{2}}$

            $=\dfrac{1-(\frac{1}{2})^n}{\frac{1}{2}}=2(1-\frac{1}{2^n})=2-\dfrac{1}{2^{n-1}}$