Triangular Numbers and Running Expressions with Equalities

In previous work ( Part I, Part II, Part III), running equalities are written in terms of 1 to 9 and 9 to 1 or 9 to 0 separated by single or double equality signs. Each digits is used once with basic operations, along with factorial, square-root and Fibonacci sequence values. These types of equalities, we called as running expressions. This work bring running expressions with double and triple equality signs using Triangular sequence numbers along with basic operations. The work is up to 3 digits in increasing and decreasing orders. Four digits onwards the results shall be studied elsewhere. See below examples and link for download the work:

re9re10re11re12

I.J. TANEJA, Running Expressions with Triangular Numbers – I, Zenodo, Open Acess, Dec 21, 2018, pp.1-142, https://zenodo.org/record/2483327.

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