The maximum number of nodes in a heap tree of degree d and depth k
A complete $d$-ary tree of depth $k$ has $d^\ell$ on level $\ell$ (where $0 \leq \ell \leq k$), so its total number of nodes is
$$
\sum_{\ell=0}^k d^\ell = \frac{d^{k+1}-1}{d-1}.
$$