Answer :
Triangular numbers are a pattern of numbers that form equilateral triangles. Each subsequent number in the sequence adds a new row of dots to the triangle.
In each case, the number of dots in the lower row increases by 1. We can depict this by:
[tex]\begin{gathered} n=1,\text{ }1\text{ dot} \\ n=2,\text{ 1+2=3dots} \\ n=3,\text{ 1+2+3=6dots} \\ \text{For T}_n=1+2+3+\ldots+n \end{gathered}[/tex]Therefore, putting this in summation form gives:
[tex]\begin{gathered} T_n=\sum ^n_{k\mathop=1}K \\ \text{where: }K\text{ = Positive integer and }T_n=triangle\text{ numbers} \end{gathered}[/tex]