Why divide by $b-1$ when computing size of a tree In one of the lectures I went to, my professor stated that in order to determine the size of a search tree, we use the following formula: 
$$\frac{b^{d+1}-1}{b-1},$$
whee $b$ is the branching factor and $d$ is the depth of the tree in question. I would like to understand why we divide by $b-1$. I would have thought that the correct solution is $b^{d+1}-1$.
There are $b^i$ nodes at depth $i$, and so the total number of nodes is
$$
1 + b + b^2 + \cdots + b^d = \frac{b^{d+1}-1}{b-1},
$$
using the formula for the sum of a geometric progression.