By E I mean sum from k=1 to n
Find a closed expression for
1+ E [1 / 2^(k-1)]
I used the formula for geo series and have the sum = 1 - 1/2^n. Is this correct? How do I make a closed expression?
You have $\displaystyle \displaystyle 1 + \sum_{k = 1}^n{\frac{1}{2^{k-1}}} = 1 + \sum_{k = 1}^n{\left(\frac{1}{2}\right)^{k - 1}}$
This sum is an infinite geometric series with $\displaystyle \displaystyle a = 1, r = \frac{1}{2}$. Since $\displaystyle \displaystyle |r| < 1$, the sum is equal to $\displaystyle \displaystyle \frac{a}{1 - r}$. Go from here.