Recurrence expansion

For recursive algorithms in computing and in mathematics, a recurrence expansion expands out each recursive term as a sum of the next terms.

For example, say we have a recursive algorithm that successively takes in half of the input array until we reach $n=1$.

$$F=c+F(n/2)$$ $$F=c+c+F(n/4)$$ $$F=c+c+\cdots +F(n/n)=c+\cdots +c$$

How many $c$ do we end up having? Since we need the number as a result of dividing $n$ by 2 to get $n=1$, we get:

$$\frac{n}{2^x}=1$$ $$x=\log n$$