Max no. of keys of B-Tree of height h I am reading about B-Tree through CLRS. One of the exercise problem is to express maximum number of keys in a BTree of height $h$ and minimum degree $t$.

Properties of BTree of $t$:


$t\ge 2$
Min. no of keys in a node is $t-1$ and max. number of keys in a node is $2t-1$
Max number of children a node can have is $2t$


To solve it the formula I came up with is $$\sum_0^h (2t)^h(2t-1) $$

Does it have any convergence?
Found it

$$\sum_0^h (2t)^h(2t-1) = (2t-1) \sum_0^h(2t)^h = (2t)^{h+1}-1 $$