Adding Fractions · Superchallenge problem

Start with $\dfrac{1}{2}$. Add $\dfrac{1}{4}$, then add $\dfrac{1}{8}$, then $\dfrac{1}{16}$, and so on, each new fraction half of the one before. How many fractions must you add together (counting the first $\dfrac{1}{2}$) before the total is more than $\dfrac{99}{100}$?