Tri Num Sum

The Sum of ten consecutive Triangular Numbers:

Starting with T0 = 0, in base 10,

The sum of the first 10 triangular numbers from T0 to T9 = 165
The sum of the next 10 triangular numbers from T10 to T19 = 1165
The sum of the next 10 triangular numbers from T20 to T29 = 3165
The sum of the next 10 triangular numbers from T30 to T39 = 6165
The sum of the next 10 triangular numbers from T40 to T49 = 10165
The sum of the next 10 triangular numbers from T50 to T59 = 15165

and so on.

The same pattern is evident in other bases [when summing T0 to Tbase-1 and so on].


• As submitted by Julian Beauchamp, 9v19, to Shyam Sunder Gupta’s “Fascinating Triangular Numbers”.