A.O. Olagunju and S. Raval (USA)
Mathematical model, mathematical induction, series.
This paper discusses the use of statistical data in generating the exact mathematical models for sums of sequences. In particular, least squares algorithms are used to generate fixed models for sums of series. The paper shows that i4 = n(n+1)(6n3 + 9n2 + n - 1)/30 and i5 = n2 (n+1)2 (2n2 + 2n - 1)/12, where the sum is computed from i = 1 to n. Mathematical induction is used to prove the correctness of these two fixed formulas. The paper discusses the steps for deriving the fixed models for geometric and exponential series. Graphs are used to illuminate the distributions of exponential models.
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