A triangular number is a number that is a sum of numbers 1 to n
n Δ = 1 + 2 + 3 + . . . + ( n − 2 ) + ( n − 1 ) + n {\displaystyle n_\Delta = 1 + 2 + 3 + ... + (n-2) + (n-1) + n}
Triangular numbers:
1 Δ = 1 = 1 {\displaystyle 1_\Delta = 1 = 1}
2 Δ = 1 + 2 = 3 {\displaystyle 2_\Delta = 1 + 2 = 3}
3 Δ = 1 + 2 + 3 = 6 {\displaystyle 3_\Delta = 1 + 2 + 3 = 6}
4 Δ = 1 + 2 + 3 + 4 = X {\displaystyle 4_\Delta = 1 + 2 + 3 + 4 = \mathcal{X}}
5 Δ = 1 + 2 + 3 + 4 + 5 = 13 {\displaystyle 5_\Delta = 1 + 2 + 3 + 4 + 5 = 13}
6 Δ = 1 + 2 + 3 + 4 + 5 + 6 = 19 {\displaystyle 6_\Delta = 1 + 2 + 3 + 4 + 5 + 6 = 19}
7 Δ = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 24 {\displaystyle 7_\Delta = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 24}
8 Δ = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 30 {\displaystyle 8_\Delta = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 30}
9 Δ = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 39 {\displaystyle 9_\Delta = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 39}
X Δ = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + X = 47 {\displaystyle \mathcal{X}_\Delta = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + \mathcal{X} = 47}
E Δ = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + X + E = 56 {\displaystyle \mathcal{E}_\Delta = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + \mathcal{X} + \mathcal{E} = 56}
10 Δ = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + X + E + 10 = 66 {\displaystyle 10_\Delta = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + \mathcal{X} + \mathcal{E} + 10 = 66}
11 Δ = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + X + E + 10 + 11 = 77 {\displaystyle 11\Delta = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + \mathcal{X} + \mathcal{E} + 10 + 11 = 77 }
