# The Triangular Numbers in Actions

• Mulatu Lemma Professor
• Daniel Lemaitre Department of Mathematics College of Science and Technology Savannah State University USA
• Rashamel Edwards Department of Mathematics College of Science and Technology Savannah State University USA
Keywords: Triangular numbers, Perfect square, Pascal Triangles, perfect numbers

### Abstract

The triangular numbers are formed by the partial sum of the series 1+2+3+4+5+6+7….+n [2].  In other words, triangular numbers are those counting numbers that can be written as Tn = 1+2+3+…+ n.   So,

T1= 1

T2= 1+2=3

T3= 1+2+3=6

T4= 1+2+3+4=10

T5= 1+2+3+4+5=15

T6= 1+2+3+4+5+6= 21

T7= 1+2+3+4+5+6+7= 28

T8= 1+2+3+4+5+6+7+8= 36

T9=1+2+3+4+5+6+7+8+9=45

T10 =1+2+3+4+5+6+7+8+9+10=55

In this paper, we investigate some important properties of triangular numbers. Some important results dealing with the mathematical concept of triangular numbers will be proved.  We try our best to give short and readable proofs.  Most of the results are supplemented with examples.

### Author Biography

Mulatu Lemma, Professor

Department of Mathematics

College of Science and Technology

Savannah State University USA

### References

1. Jones K, Parker S, and Lemma M: The Mathematical Magic of Perfect Numbers: GaJSci 66(3): 97-106, 2008
2. Gupta S: “Fascinating Triangular Numbers” : p3, 2002
3. Hamburg C: “Triangular Numbers Are Everywhere!”: Illinois, Mathematics and Science Academy: p5, 1992.
Published
2021-12-01
How to Cite
Lemma, M., Lemaitre, D., & Edwards, R. (2021). The Triangular Numbers in Actions. GPH - International Journal of Mathematics, 4(11), 01-11. Retrieved from http://gphjournal.org/index.php/m/article/view/507
Section
Articles

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