Total number of nodes in a tree data structure?

Question

I have a tree data structure that is L levels deep each node has about N nodes. I want to work-out the total number of nodes in the tree. To do this (I think) I

Answer 1

Ok, each node has about N subnodes and the tree is L levels deep.

With 1 level, the tree has 1 node.
With 2 levels, the tree has 1 + N nodes.
With 3 levels, the tree has 1 + N + N^2 nodes.
With L levels, the tree has 1 + N + N^2 + ... + N^(L-1) nodes.

The total number of nodes is (N^L-1) / (N-1).

Ok, just a small example why, it is exponential:

                    [NODE]
                      |
                     /|\
                    / | \
                   /  |  \
                  /   |   \
            [NODE]  [NODE] [NODE]
              |
             /|\
            / | \