The sequence of the power combination of expansion of the Kifilideen trinomial theorem of positive power of N is arranged in groups and patterns. Having a clearer view or picture of how the formulas of the components of the Kifilideen trinomial expansion were derived can lead to the discovery of formulating formulas for the series and sequences which follows the same pattern of progression as that of the trinomial expansion where series and sequence are not generated from trinomial expansion. Therefore, this study provides derivation for the formulas of the components of the Kifilideen trinomial expansion of positive power of N with other development. The research work also inaugurated Kifilideen theorem of matrix transformation of Newton’s binomial theorem of positive and negative power of N and – N where a and b are found in parts of the Newton’s binomial expansion of the positive and negative power N and – N. The idea of series and sequence were employed in developing the formulas of the components of the Kifilideen trinomial expansion of positive power of N. The study indicates that there are sequences and series that can be developed which are not trinomial based but have the same pattern in term of progression as that of the latter. The Kifilideen theorem would ease the method of obtaining the power combination of a given term of Newton’s binomial expansion in a systematic way.

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APA

Lekan Osanyinpeju, D.
(2022). DERIVATION OF FORMULAS OF THE COMPONENTS OF KIFILIDEEN TRINOMIAL EXPANSION OF POSITIVE POWER OF N WITH OTHER DEVELOPMENTS. *Afribary*. Retrieved from https://afribary.com/works/derivation-of-formulas-of-the-components-of-kifilideen-trinomial-expansion-of-positive-power-of-n-with-other-developments

MLA 8th

Lekan Osanyinpeju, Dr Kifilideen
"DERIVATION OF FORMULAS OF THE COMPONENTS OF KIFILIDEEN TRINOMIAL EXPANSION OF POSITIVE POWER OF N WITH OTHER DEVELOPMENTS" *Afribary*. Afribary, 09 Jun. 2022, https://afribary.com/works/derivation-of-formulas-of-the-components-of-kifilideen-trinomial-expansion-of-positive-power-of-n-with-other-developments. Accessed 07 Aug. 2024.

MLA7

Lekan Osanyinpeju, Dr Kifilideen
. "DERIVATION OF FORMULAS OF THE COMPONENTS OF KIFILIDEEN TRINOMIAL EXPANSION OF POSITIVE POWER OF N WITH OTHER DEVELOPMENTS". *Afribary*, Afribary, 09 Jun. 2022. Web. 07 Aug. 2024. < https://afribary.com/works/derivation-of-formulas-of-the-components-of-kifilideen-trinomial-expansion-of-positive-power-of-n-with-other-developments >.

Chicago

Lekan Osanyinpeju, Dr Kifilideen . "DERIVATION OF FORMULAS OF THE COMPONENTS OF KIFILIDEEN TRINOMIAL EXPANSION OF POSITIVE POWER OF N WITH OTHER DEVELOPMENTS" Afribary (2022). Accessed August 07, 2024. https://afribary.com/works/derivation-of-formulas-of-the-components-of-kifilideen-trinomial-expansion-of-positive-power-of-n-with-other-developments