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Consider a tetrahedral stack of spheres as in this image:

Suppose there is a stack consisting of $n$ layers, and the spheres all have diameter $d$.
Showing your work:
a) Compute the number $N$ of spheres in the stack as a function of $n$. Then, express $N$ as a binomial coefficient.
b) Compute the height $h$ of the stack as a function of $d$ and $n$.

Suppose there is a stack consisting of $n$ layers, and the spheres all have diameter $d$.
Showing your work:
a) Compute the number $N$ of spheres in the stack as a function of $n$. Then, express $N$ as a binomial coefficient.
b) Compute the height $h$ of the stack as a function of $d$ and $n$.