Square triangular number: Difference between revisions

Revision as of 06:05, 28 May 2024

Revision as of 05:33, 14 June 2024

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{{bi|left=1.6|<math>\displaystyle N_k = s_k^2 = \frac{t_k(t_k+1)}{2}.</math>}}

Define the ''triangular root'' of a triangular number <math>N=\tfrac{n(n+1)}{t2}</math> to be <math>n</math>. From this definition and the quadratic formula,

{{bi|left=1.6|<math>\displaystyle n = \frac{\sqrt{8N + 1} - 1}{2}.</math>}}