Abstract
Mathematical series play an important role in various aspects of our life and help to predict, evaluate and monitor the outcome of a situation in order to pass decision. The purpose of this paper is to develop a new kind of series and the sum or deduction of two terms of which fractionally cancel in order to get the cancellation result <img src=image/10.5923.j.ajms.20211103.01_001.gif></img>. let for all <img src=image/10.5923.j.ajms.20211103.01_002.gif></img> and let <img src=image/10.5923.j.ajms.20211103.01_003.gif></img> such that <img src=image/10.5923.j.ajms.20211103.01_004.gif></img> and <img src=image/10.5923.j.ajms.20211103.01_005.gif></img> then <img src=image/10.5923.j.ajms.20211103.01_006.gif></img>.
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