# Our Brief Journey with properties and patterns of Triangular Numbers

• Angelo Nickerson
• Mulatu Lemma Professor
Keywords: Triangular Numbers

### Abstract

The triangular numbers are formed by 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 some important properties of triangular numbers are studied.

### Author Biographies

Angelo Nickerson

Department of mathematics

College of Science and Technology

Savannah State University

USA

Mulatu Lemma, Professor

Department of Mathematics

College of Science and Technology

Savannah State University USA

### References

Stephanie Parker, Mulatu Lemma, the Mathematical Magic of PerfectNumbers. Georgia Journal of Science

Maths, T. (2014, October 09). Triangular Numbers: EYPHKA. Retrieved August 31, 2020, from https://thatsmaths.com/2014/10/09/triangular-numbers-eyphka/

Triangular Number Sequence. (n.d.). Retrieved November 02, 2020, from https://www.mathsisfun.com/algebra/triangular-numbers.html

McMartin, K., & McMaster, H. (n.d.). Opening the door on Triangular numbers. Retrieved November 11, 2020, from https://files.eric.ed.gov/fulltext/EJ1121175.pdf

https://www.mathsisfun.com/pascals-triangle.html

Weissman, E. (n.d.). Binomial Coefficient. Retrieved November 09, 2020, from https://mathworld.wolfram.com/BinomialCoefficient.html

Gregerson, E. (n.d.). Binomial theorem. Retrieved November 09, 2020, from https://www.britannica.com/science/binomial-theorem
Published
2021-02-01
How to Cite
Nickerson, A., & Lemma, M. (2021). Our Brief Journey with properties and patterns of Triangular Numbers. GPH - International Journal of Mathematics, 4(01), 11-22. Retrieved from https://gphjournal.org/index.php/m/article/view/344
Section
Articles

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