# Triangular Numbers in actions

• Aaliyah Walters
• Mulatu Lemma Professor
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 In other words, triangular numbers are those counting numbers that can be written as = 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 Biographies

Aaliyah Walters

Department of Mathematics

Savannah State University

USA

Mulatu Lemma, Professor

Department of Mathematics

College of Science and Technology

Savannah State University USA

### References

Triangular number sequence. (n.d.). Retrieved February 02, 2021, from https://www.mathsisfun.com/algebra/triangular-numbers.html
Maths, T. (2014, October 09). Triangular Numbers: EYPHKA. Retrieved August 31, 2020, from https://thatsmaths.com/2014/10/09/triangular-numbers-eyphka/
Jones K, Parker S, and Lemma M: The Mathematical Magic of Perfect Numbers: GaJSci 66(3): 97-106, 2008
Hamburg C: “Triangular Numbers Are Everywhere!”: Illinois, Mathematics and Science Academy: p5, 1992.
Published
2021-04-30
How to Cite
Walters, A., & Lemma, M. (2021). Triangular Numbers in actions. GPH - International Journal of Mathematics, 4(04), 32-44. Retrieved from http://gphjournal.org/index.php/m/article/view/402
Section
Articles

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