Inducing the sum of the Fibonacci sequences from the Moment of Inertia of an Object
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Abstract
By employing the Parallel Axis Theorem for a thin rod, we derive a refined identity that is applicable to an arbitrary sequence. Through the substitution of diverse general sequences within this identity, we establish novel sums of Fibonacci sequences.
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References
[1] K. Adegoke, Sums of fourth powers of Fibonacci Lucas numbers, arXiv:1706.00407. https://arxiv.org/pdf/1706.00407 Google Scholar
[2] S. Falcon and A. Plaza, On the Fibonacci k-numbers, Chaos, Solitons Fractals 32 (2007), 1615–1624. https://doi.org/10.1016/j.chaos.2006.09.022 Google Scholar
[3] A. F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quart. 3(3) (1965), 161–176. Google Scholar
[4] H. Ohtsuka and S. Nakamura, A new formula for the sum of the sixth powers of Fibonacci numbers, Congr. Numer. 201 (2010), 297–300. https://vixra.org/abs/0910.0012 Google Scholar
[5] D. Treeby, Further physical derivations of Fibonacci summations, Fibonacci Quart. 54 (2016), 327–334. Google Scholar
[6] V. Verma and P., Properties of 2-Fibonacci sequence, J. Phys.: Conf. Ser. 2267 (2022), 012153. https://doi.org/10.1088/1742-6596/2267/1/012153 Google Scholar