ISSN: 2375-3927
International Journal of Mathematical Analysis and Applications  
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An Alternative Method for Deriving Infinite Series Using Long Division for School-Aged Students
International Journal of Mathematical Analysis and Applications
Vol.5 , No. 1, Publication Date: Feb. 12, 2018, Page: 35-38
1344 Views Since February 12, 2018, 521 Downloads Since Feb. 12, 2018

Nicoladie Tam, Department of Biological Sciences, University of North Texas, Denton, Texas, USA.


The equivalence of an infinite series, such as (0.999… = 1) to a finite number is often not intuitively obvious to understand for most students. Yet, it is helpful to use an intuitive method to derive the equivalence that is familiar to most elementary school students. In this paper, a simple proof of the equality of 0.999… and 1 is provided by a non-traditional method using long division with an alternate quotient. This alternate method that uses long division to prove an infinite series of numbers can stimulate the imagination of students to use abstraction to understand the mathematical concept of infinity. This can be done without the use of geometric series.


Infinite Series, Division, Geometric Series, Quotient


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