# Tetrahedral number Calculator

## Calculates the number of balls and the height in a regular tetrahedron.

number of stages
 1,2,3,...

total balls Tn
height to accumulate hn
 ( diameter of a ball =1 )
 $\normal Tetrahedral\ number\\\vspace{5}(1)\ total\ balls\\\hspace{40} T_n={\large\sum_{\small k=1}^n\frac{k(k+1)}{2}}={\large\frac{n(n+1)(n+2)}{6}}\\[10](2)\ height\ to\ accumulate\\\hspace{40} h_n=\sqrt{\large\frac{2}{3}}(n-1)+1\\$

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