triangular number is a number that is a sum of numbers 1 to n

${\displaystyle n_\Delta = 1 + 2 + 3 + ... + (n-2) + (n-1) + n}$

Triangular numbers:

${\displaystyle 1_\Delta = 1 = 1}$

${\displaystyle 2_\Delta = 1 + 2 = 3}$

${\displaystyle 3_\Delta = 1 + 2 + 3 = 6}$

${\displaystyle 4_\Delta = 1 + 2 + 3 + 4 = \mathcal{X}}$

${\displaystyle 5_\Delta = 1 + 2 + 3 + 4 + 5 = 13}$

${\displaystyle 6_\Delta = 1 + 2 + 3 + 4 + 5 + 6 = 19}$

${\displaystyle 7_\Delta = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 24}$

${\displaystyle 8_\Delta = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 30}$

${\displaystyle 9_\Delta = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 39}$

${\displaystyle \mathcal{X}_\Delta = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + \mathcal{X} = 47}$

${\displaystyle \mathcal{E}_\Delta = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + \mathcal{X} + \mathcal{E} = 56}$

${\displaystyle 10_\Delta = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + \mathcal{X} + \mathcal{E} + 10 = 66}$

${\displaystyle 11\Delta = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + \mathcal{X} + \mathcal{E} + 10 + 11 = 77 }$

Properties

• A triangular number does not end on 2,5,8 or E.