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Tetrahedral Numbers

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Calculates the tetrahedral number: the total number of balls stacked in the shape of a regular tetrahedron.
Number of layers stacked: n
Layer
Total number of balls Tn 
Stacking height hn 
(Assume the diameter of the ball is 1.)
\(\normalsize Tetrahedral\ number\\ (1)\ total\ balls\\ \hspace{40px} T_n={\large\displaystyle \sum_{\small k=1}^n\frac{k(k+1)}{2}}={\large\frac{n(n+1)(n+2)}{6}}\\ (2)\ height\ to\ accumulate\\ \hspace{40px} h_n=\sqrt{\large\frac{2}{3}}(n-1)+1\\ \)

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