Mathematical Study on Alternating Series in a Regular Hexagon–Proof without Words

Exploring a Novel Proof Method for Summation of Alternating Series in a Regular Hexagon

by Debajyoti Goswami*,

- Published in Journal of Advances and Scholarly Researches in Allied Education, E-ISSN: 2230-7540

Volume 16, Issue No. 4, Mar 2019, Pages 1740 - 1740 (1)

Published by: Ignited Minds Journals

ABSTRACT

The aim of this paper is to introduce a new approach to prove the sum of an alternating series. This is an approach to prove the sum of an alternating series in a regular hexagon.

KEYWORD

mathematical study, alternating series, regular hexagon, proof without words, sum, new approach

1. INTRODUCTION:

The proof of the sum of an alternating series in words was introduced a long time ago. Then the study on alternating series to prove without words was started. In 2009 Unal Hasan introduced the proof of the sum of an alternating series without words. In 2012 R B Nelsen introduced the sum of an alternating series in a square. Being inspired from their papers in this paper I shall introduce a new approach to prove the sum of an alternating series. I shall prove the sum of the alternating series in a regular hexagon without words.

2. PRELIMINARIES:

We know that the sum of the alternating series 1-(1/2)+(1/4)-(1/8)+(1/16)-………..… is 2/3.

3. NEW APPROACH:

Now we prove the sum of 1-(1/2) + (1/4)-(1/8) + (1/16)-…………is 2/3 without words in a regular hexagon. Thus the sum of the given alternating series is 2/3. Hence we prove that 1-(1/2)+(1/4)-(1/8)+(1/16)-…….=(2/3) in a regular hexagon without words.

REFERENCES:

1. R.B. Nelsen (2015). Proof without words III: Further Exercises in Visual Thinking, The Mathematical Association of America, pp. 160-161. 2. R.B. Nelsen (2012). Proof without words: An alternating series, College Mathematics Journal 43(5), p.370. 3. Unal Hasan (2009). Proof without words: Sum of an infinite series, College Mathematics Journal 40(1), p.39.

Corresponding Author Debajyoti Goswami*

Research Scholar, Department of Mathematics, Dr. A.P.J. Abdul Kalam University, Indore