Imagine that we have to calculate the number of branches of a tree. Now I made a formula that associates the "level" (number of the times that a branch replicates itself) $k$ of the tree and the "growth" of the branches $g$ of the tree for example:
Now at the beginning I thought that the formula was something like $\sum 2g$ or $\sum 2k$ but now I think that the formula is: $$S_{g;k}=\sum_{i=0}^{k-1} g^i$$
Is this correct?