Sunday, December 27, 2015

Tr(n)^2+Tr(n+1)^2=Tr((Tri(n) + Tri(n+1)) for triangular numbers

I found this about the triangular numbers, also known as the number of distinct pairwise combinations of n items or the sum of the first n of 1,2,3,4,... this wasn't listed on the Encyclopedia of Integer sequences... , The formula for a triangular number is:

I found that:

Provable easily by substituting the formula for Tri in each side:

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